Hey, how are you guys today? I'm super excited that you've joined us to the Realty Success Hub I'm Angela Brown and I represent the cleaning end of the move-in move-out clean business And today I have two special realtors with me and I say they're special because they're gonna answer a lot of our Questions that house cleaners typically have when they go to try to buy a home and you have credit issues or you have You know proof of income issues or all that kind of stuff So I'm super excited about today's session and I know a lot of you have jumped in and you've sent me your questions in advance So please help me welcome Brooke Bryant Brooke jump in and introduce yourself Tell us who you are tell us where you are and a little bit about what we might expect from you today So I'm Brooke Bryant. I'm a realtor in Charlotte, North Carolina in the surrounding area I love working with first-time home buyers So I get a lot of these these Situations where people are working on rebuilding their credit or repairing their credit or just starting out with no credit and Love to help them try and find the answers to all those situations And I'm gonna step off camera for one minute and move my car to let someone out.  All right. How about you Aaron? Yes, I'm a realtor in the greater San Antonio area We we cover the greater area and so Yeah, been doing real estate for quite a few years and really enjoy the process I get to work with a lot of first-time home buyers as well And here primarily the market is veterans Military veterans and so we work tremendous a lot with military veterans as well So we're excited to answer some questions today and get into the financing details of real estate Well, you know, I'm so glad that you brought that up about the veterans as well Because we we run into a lot of situations where there are first-time home buyers and there are a lot of questions And I know that there are a lot of fears of especially in the house cleaning industry where homeowners and house cleaners are You know, how do I buy a home? If this is the first time I've ever done it especially in the house cleaning industry where you may not have excellent credit Or where you don't know what is involved and what you're gonna need to come to the table with So I have a I have a couple of things that I want to run by you And I don't know if there's a best place to start or do I just start firing questions at you or how does that work? Love love questions. Let's let's jump into some questions. The reality is when you purchase a home It's it's kind of all over the place as far as where people are coming from and so Love to answer any questions as they come up Well, the first question that I have is about the credit score And the reason that I bring up the credit score is because I know that a lot of people that are getting involved in the house Cleaning industry are getting started in the cleaning industry either because there were credit issues or because as they were Starting to do their business Hey, welcome back Brooke. See you again As they were getting started in the cleaning business either they were in debt and they were looking for some fast cash or they were Just starting a business because this is what they wanted to do in life. And so like there is no credit history yet Can you just go buy a house or do you need to like have a certain credit history? Like what what does that look like for somebody that's just starting out? Well, I want to preface this by saying I'm not a lender but I do get to work closely with lenders and so What we have found in our experience is that lenders are typically looking for a 24 month history of income and So in most cases and there are always exceptions to this rule But in most cases lenders are looking for a 24 month history in the same type of industry So whatever business you're in if you've got a little bit of history over time Even if you have low to no credit They can often get you on a program that would help you, you know get to your first milestone pretty quickly But usually they're looking for about 24 months. Now again, there are exceptions to that rule There are business loans. There are bank loans portfolio loans, etc. They give other options to that and Again, depending on your situation, we could always pair you with a lender that specializes in your situation But by and large on average about 24 month history Okay, so let's let's throw a monkey wrench at you Let's say that I want to buy a house and I'm just starting my cleaning business and I don't have a 24 month history and I I kind of have good credit, but I don't really know if I have credit good enough to buy a house What what is the barometer of what I have to have in order to come to the table to even have a conversation with the Rilter and either of you can answer that Well You do need to know What your credit score is and that is going to determine the type of loan that you get and Typically the higher your credit score The lower interest rate you're going to pay The better the terms of your loan are going to be a conventional loan you need to have a score of What 620 for a conventional loan? There are Like Aaron said lenders want to see a History of your work history for 24 months. There are Loans that someone can get Low dock loans. They're not They used to be more common, but you know back in the prime lending days and all that But there are low dock bones that you can get that not every lender provides those you'd have to have a really high credit score For that like in the 700s and they can use bank statements rather than your tax returns and they're You're gonna have to jump through more hoops because you're You just kind of have more to prove With those situations and that's why when your credit is lower You're trying to prove to the person who's giving you that money who's loaning you that money that you are going to pay it back So it's so they're there are products out there for folks who don't have a 24 month History that they can show with tax documents, but you're gonna have to have a higher credit score and typically more money down to So in this picture, there's 732 which is the credit score on the picture. Do I have to have a 732 credit score in order to buy a house? No They're actually lenders that will go as as low as 580 On your loans here again, you're gonna get better rates the better your score is And so you're gonna pay higher interest rates the lower your score is and again, you're a higher risk factor to the lender at that point It's always a good idea to sit down with a realtor though and talk about your options because based on where you're at They could probably pair you with somebody who could help you get to your destination the quickest If you feel like your credit score is below that 580 Then we can get you with a repair program credit repair program something like that And get you on the right foot usually within, you know, three to six months We can get your score within the range that you would qualify. It may not be the best terms But again kind of depends on your life and what's going on and how quickly you want to move So a quick consultation would help flush some of those issues out and get you off on the right foot So if that's the case and I was gonna have a consultation and Suppose that I'm a new house cleaner that's just getting involved in the industry And I'm trying to pull together my paperwork and I'm trying to make everything above board and I'm trying to You know build my credit and all that stuff Is it better to have the conversation first with the lender or is it better to first have it with the realtor And get like the you know get locked in on a home and get the pricing and all that stuff And then have a conversation with the lender to see if it's even possible What what is the first step for that to have to have to happen? I'm a little I'm a little biased on that because Most lenders will pull your credit right away to see where you're at And if they're pulling your credit, it's going to drop it by a couple of points because it's a hard inquiry to start with Even though if you're home shopping you can pull it from multiple sources over a short period of time like a 30-day time frame And it's not going to keep lowering that score It I would recommend sit down with your realtor first And really flush out your goals your time frame you're moving So we can see when it's best for you to get your score your score pulled And whether we're just looking at pulling your FICO or whether we need a more in-depth search And go with a different type of lender that's going to look at assets and Liabilities and other things surrounding your life as opposed to just a FICO score Which is typically what a bank will do is just you know run your FICO score right quick and see where you're at So but to piggyback on that I always advise clients very often I'll have clients who want to go out look at homes Before they've ever met with a lender And I don't like to do that because your your buyer client will very often fall in love with something that It's just not obtainable for them. And then anything less than that can feel like a letdown So, um, it's I think it's great to talk with your realtor Determine what your goals are have your realtor recommend some lenders who they've had experience with who know May be able to help you with your particular situation And and get that get that part of it settled get your financial Goals on track before you go out to look at homes So I don't want to string any realtors along so I'm going to ask a question that Needs to be asked But let's say that I have Questionable credit and I might be able to get a loan from a special program But I don't know Is it is it cool to call a realtor and say hey, I'd like you to be my realtor and I I'm going to be honest with you up front I've got these credit issues and I may or I may not qualify and then Get them involved in the process of helping you when maybe it may not turn into a deal at all I mean, I don't I don't want to string a realtor along for a couple of months while they help you rebuild your credit Or they're they're pulling loans for you and trying to make deals happen And then it never happens for the realtor because then I would feel bad for them I don't see that as stringing along. I think realtors Part of what we do is we develop long-term relationships so we can help that that client Along their journey of of achieving home ownership. So You know, no, I wouldn't have a realtor drive around with you Eight hours every weekend for a month Not knowing, you know looking at homes and not knowing if you can qualify to get a loan for it But you know, I think establishing that relationship Even before you're in a position to buy I think it's that's never a bad idea Now when you go to the realtor, okay, so let's say that that's the case I'm going to go get me a real I'm going to go get me a realtor Do you do you need to have a down payment down of what you're prepared to pay? Or is it is it okay to just show up and say, hey, I would like to start the process and I don't know what I need and so Can you can you help me get started? I mean like What what what happens and what? We we offer free consultations before I ever take a client out to actually look at a home I like to sit down with them over coffee and really set expectations and figure out what's going on in their life That's peripheral to just buying a home because oftentimes it's a lot of it's it's your whole life It's your life issues. It's things that are going on in your life and those all play a role into Your time frame and what you're wanting to do if you're in a lease, etc And so really the best place to start is sitting down and having that consultation It's free is something we love to do and it helps us give you a realistic time frame And the best route for you to get to where you want to be And like I say, you know, whatever your dreams or goals are I want to be in this neighborhood this type of house, etc We can get you there with the white people But we have to get really clear on expectations and what you're wanting long term in order to make that work And so I love sitting down with a client first And having that, you know, 30 minute conversation getting in depth into your life And figuring out what's going on with you and how best we can help and if we're the right fit So if I have assets like let's say that I have a 401k from a previous job Is that something that I could use as a down payment towards my house? And how do I know if if I have anything that I could use as a down payment or any anything of any equitable value Is that something that I bring to the table right up front or do I kind of wait until I see what you can do as a realtor first and what kind of loans you can help me put together and then bring that kind of as a Sweet in the pot kind of thing I mean, I'll let brook take this in just a minute. But what I do want to say is The more open you can get with your realtor The faster we can get you to where you want to go um There there's a difference between A customer and a client in our business a client interest into a relationship that's under our care and protection And is our fiduciary responsibility to look out for your best interests And as a customer, you're just shopping. You might be talking to multiple realtors And there's no vested interest on either side in that It's more of a coffee general conversation Wish you the best of luck if we can help great If you want to become my client Then we get really in depth about your finances your credit score your family your lifestyle schools You know traffic patterns, etc. How long do you want to spend in the car? Do you like that our ride, you know away from your family so you can relax and be you know, normal when you get home all those kinds of things and so really We get really in depth, but you have to You have to really trust your realtor that they're going to take you down that road And that's part of the idea of a consultation Is really getting on the same page and seeing if we're the right fit if we're the right personality If if we're going to be able to work together for three months six months a year However long it takes to get you to where you want to go and then ultimately hopefully be friends over time And so i'll throw that over to you bro. But yeah Yeah, it's a very personal relationship And I don't know if this is the case with you erin sometimes very often I'll have friends or family who don't want me to represent them as their realtor because you do Get to see parts of their lives that they may not want you as a friend to see You do have to to expose yourself and it's all going to come out in the wash So like erin said be as transparent as you can be i've had Transactions where we were the day before we were closing the lender discovered that My client the buyer had um unreported. They had he had child support That he was obligated for and wasn't disclosed. So Yeah, it prevented him from being able to get that loan and close on the house. So it's going to come out in the wash. So Just lay it all out there because at the end of the day what you want is is to own a home and let's just You lay it all out there and dig through it and figure out a way to make that happen And and those those consultations that erin mentioned Can be very empowering for our clients too if if you are a housekeeper you've started your business But let's say you've got a partner who has been in the military They may qualify for a VA loan and have to put no money down And you know, they just they weren't thinking about about that like oh well, I They're two of us buying it So having those conversations getting to know each other getting to know what your dreams are and how you can accomplish those You can learn a lot through through those consultations and you mentioned 401k You you can use a 401k depending on where you are in life. There may be penalties for that Um, but that money is yours and it's available for you to use And and meeting with a lender will help you determine Is that your best bet? Are you a first-time home buyer? Would you qualify for a down payment assistance program? so, um, there's lots of options lots of options and Just I want people to be aware of that. There's A generally a solution for every problem. It may not be a solution that will get you in a home this month But knowing what's out there will help put you on the right path to get you to to achieve your dream I know that there are a lot of business owners their first-time business owners and so as a business owner of a cleaning company I know a lot of times they're thinking either i'm not going to qualify for a house because they've got kind of a cash business And I maybe they haven't reported all of their income or maybe It's a skinny paper trail or something like that What does a startup business need to do in order to pull all their resources together before they they contact you and say Okay, look, I'm ready to buy a home. I think I have this that I can use as a down payment I have I think erin mentioned you've got to have two years of bank statements that you can bring and say This is the income money that I have coming in like what what else is needed in order to show up and be totally transparent about the income that's earned and what is available for a down payment and Being realistic about these are the debts that I have and this is You know that like you said the child support and all that stuff What is needed from a house cleaning business owner to show up to the table and just be honest and transparent about that process I'll throw this to brook it just a second Something that we run into a lot Is you know people come to us and say hey, I'm saving up for a home And I said well Tell me a little bit about that and they're like well my my uncle joe my uncle bob said I'm supposed to save x amount Well depending on the loan type That would change entirely And depending on your situation that would change entirely And then a lot of people don't calculate in closing costs or title costs or any of those other things and so Oftentimes people are saying hey, I'm saving for a home But yet they have no idea how much they actually need to bring to the table And so we run into that a lot where people are like I've been saving for five years It's like great. You could have already bought two homes, you know, right? And so Brooke what do you have to say about that? Again knowledge is power So talk with realtor let like your realtor know what you're looking for and then bring a lender into that And the lender can help estimate those closing costs How much money you're going to have to have an escrow which is generally six months or a year of your your homeowner's insurance and your The taxes on your home And they can help you create a budget for that this is realistically what you're going to need to bring to the closing table No, you may not need Um 20 down there are loan products out there 3% down or three and a half percent for fha depending on your credit. So Yeah, the down payment really depends on the type of loan product that you're getting and also the documentation that you need if you're a business owner As much as you can possibly provide them the two years is great and but there may be loan products out there that there So many other there's your debt to income. There's your credit score your credit history So they're gonna they're gonna look at your whole financial picture Determine the best loan product for you and figure out a way to To make that happen. Um, so if if you can't make that happen in the next 90 days what do we need to do to Get you on the right track to to get you the documentation that you need to improve your credit to where you need to To have have enough money in the bank to have the down payment that you want to have the Be prepared to pay your closing cost so just Knowing what what all is out there What your what your goals are and having those conversations to create a roadmap to to make those happen to achieve those Oh, these are great answers. I just love this you guys I got a question about the pre-approval process Is it important to have a pre-approval from a loan or a lender before I Go looking for a house Or once the conversation has happened with the realtor that I'm in a better position to go ahead and look for a house Then once I have the pre-approval or how does that all work? Well in the charlotte market It's it's really competitive So if I were to take you out tomorrow to look for homes you find one you like There's a good chance that it's going to go under contract where it may have multiple offers It's not as competitive as it was a year ago But it is competitive competitive and any time I submit an offer I submit a pre-approval letter with it and generally the seller is going to want a pre-approval letter with your offer so Again in my mind it doesn't make any sense to go look at homes and you fall in love with one And you're not going to be able to obtain the financing for it So if I was going to get a pre pre-approval, is that something that I do or is that something is my realtor that you helped me with? Your realtor can put you in touch with a lender, but that is a document that you get from your lender. They It's a it's a cursory look at your finances to determine Your ability to obtain obtain a loan and a certain price range Got it. Okay And do I do I need a certain level of income in order to get a pre-approval or a certain credit limit in order to get a Pre-approval letter or is this just them them running my credit score and taking a look and just seeing where I am Yeah specifically Yes, all of those are Are things that come into play that the lender is going to best be able to handle that When you're talking about getting a loan it really comes down to The loan product that's best for you And again, it really comes down to the lender because there are lenders that specialize specifically in loan types Lenders can do any loan type, but they have specialties that they'll get you the very best rates and discounts on And so it's really getting with pairing you with the right person you need for what you're trying to do And and it will help you If if you're getting an fha loan, which is a government backed loan You can get an fha loan for three and a half percent down And the credit score is not as high. I think it's what a 580 for an fha loan Going slow. Yeah, I can go that low But yeah as low as but depending on your credit score That's going to determine your interest rate, which is going to determine how much home you can buy It could make a difference between you buying a $200,000 home And a $250,000 home depending on your credit score. So the lender is going to factor all of that in and give you kind of a window of Okay, you can afford we could Potentially Approve you for $250,000 loan that doesn't mean that yeah, we're going to give you $250,000 There's still underwriting and loan conditions and and all of that But realistically we feel like with your credit score you could afford a $250,000 home So that's what you're good.  Right Right Yeah, and it sets expectations for the buyer too. You know, I don't want to go look at A million dollar home if I can only afford a $200,000 home Uh-huh, you know, I need to have my expectations in place, too Yeah, inevitably you'll go out and fall in love with a home Um, and if it's not in your price range or not comfortable for your lifestyle We see this a lot here in my area where People want to buy a larger home than they then would actually fit their lifestyle And with all that being house poor Um, now you have to take on an extra job both spouses have to work to pay that mortgage because you just You you wanted a more home than you could actually afford And well, and I think that comes from a place of greed. I mean like of course Yes, I want the bigger home, right?  What's the rule there? Basic rule of thumb is 700 square foot per person And so kind of depending on how many people are in the home You need kind of a minimum of 700 square feet in an ideal world Um, and so that's that's kind of age it Um, and then based on your income You know would depend on where you end up a lot of people come to me and say hey I can afford x a month, you know, I'm I tapped out at 3 000 a month on my mortgage. So I can't go above that So it really comes down to you know, what works best for your lifestyle I will say in the loan approval process Um, a pre-qualification is okay, but in a competitive market, it's not competitive Don't even submit offers usually with a pre-approval We'll actually get the person to go through underwriting first so that we can present a fully underwritten offer Which means all the financing is in place and they're not going to back out due to financing Because that due diligence has already been done Pre-approval is a very basic. Hey based on what you've told us We think you can approve for x But we don't have any documentation yet to prove that And once you get under contract, then we'll put our team to work and figure out what you can actually afford and You know sometimes deals fall apart in that process And so we work diligently to get people through that Into a full approval when we're out making offers in a competitive market So does does the pre-approval have anything to do with the different loan types that you guys were talking about? I know brook had mentioned like an fha loan or a veteran's loan Does the pre-approval come into play there or are those loans possible without having a pre-approval? well our the north carolina contract asks Specifically what type of loan your buyer is getting their paying cash if they're getting fha va or conventional That can change during the course of the transaction And like erin said with the underwriting process In that situation where I had the client who had another financial obligation that wasn't disclosed If the underwriting process had been done That wouldn't have happened but Um I forgot what you said I was wondering about I was wondering about the different types of loans and do you need a pre-approval or is it is it possible that that as a Business owner I could just trust my realtor and say hey put me in touch with the best kind of loan that I might qualify for so just kind of overview a conventional loan is for folks with Typically a higher income and a higher credit score an fha loan is um it can Accommodate buyers with credit as low as 580 um and it's geared towards um lower to mid-income buyers Then there are usda loans which are typically in more rural areas It's a zero percent down loan product and then there are va loans, which is funded backed by the veterans administration that also is a zero percent loan so your you will qualify for one of those loans so You know if you've got a credit score that you can get a conventional loan You're probably going to have likely a better interest rate So you're going to want to qualify for a conventional loan that is in a in a competitive market If you're not paying cash Then buyers i'm sorry sellers like to see conventional because um, it's less stringent of an underwriting process so less likely um for for the transaction to fall apart And often less for the seller to be required to do for the buyer. So yeah your lender is going to qualify you for a specific loan product conventional usda f FHA va So yeah, um, you're the lender will do that And does the loan that I get as a cleaning business owner does that depend on the amount of down payment that I have Or is the loan independent of that or does it all work together? How does how does that work? Yeah, um, it's a great question It's it's actually based on what you've claimed on your taxes What your debt to income ratio is and how long you've been in business coupled with your credit score So there's a lot of factors that are involved and then if you have anything that could be If you have any assets that could also be used There are some outlier loans depending on your business type That maybe it's a bank statement loan or maybe it's a portfolio loan Maybe it's a bridge loan. So there's some other types of loans that can play a role in that Kind of depending on your assets what you can bring to the table and where you're at Um, but yeah, there's there's some factors there that that come into play and if you work with a really good lender They will put those puzzle pieces together and find you the perfect product for your situation Um, what we have found in our experience is most banks Don't really want to take the time to do that and I'm again, I'm not saying anything bad about banks There's some phenomenal banks out there. It's just that banks do banking And they usually have a very small mortgage department It's usually in a corner office somewhere that has a very large region And a huge stack of documents that they're working off of Um, if you work with local lenders that your realtor has worked with on a lot of clients Then they can get a lot more personal with you Figure out more what's going on in your life and look at more than just a fight go score And really get in depth for you on specifically what you need Yeah, uh, and I agree I agree erin I kind of look at it like the banks are the general practitioner of doctors and if if you You've Easy peasy you fit into this box. They're they're great. They're wonderful to work with But if you have some more specialized finances some more complicated finances some issues that you need to overcome Then you might want to go to a specialist which are these lenders that your realtor like erin said has likely had some experience with that can help you um with your specific Situation and sometimes the first lenders not always but I'm sure you've seen it happen erin This lender couldn't get it closed but you take it to another lender and they can they have Different areas of expertise or different loan products. They have access to our different knowledge and And they can get it closed when another one couldn't doesn't mean that other one wasn't a phenomenal lender It just means that they didn't have Specifically the product that you need so so so don't give up Yeah, and specifically with businesses because I know we're talking businesses here Specifically with businesses It's really important to get with a specialized lender That can really help you with your business if you're a nurse for example if you're a doctor if you have your own Practice like in the house cleaning business would want to get you with someone specialized so that they can help you get that worked out Yeah, I know this is kind of it may take some work to to pull together the information that they need to make it happen, but But that's what you need to know Normally what we run into with business owners is they're trying to mitigate taxes So they're trying to be less in taxes which show less on the books And then they're saying hey would it make sense for my business to purchase this as an asset? And can I get anything on as a tax write-off? But your business has to show income and so again working with the right lender to figure out those pieces And what you should claim and what you shouldn't etc will get you into the right house Mm-hmm Shilan says can a 20 year old secure a home loan and if so how? Yes, absolutely, and and I'll give this to brook in just a second 20 year olds definitely can when we see people purchasing in that like 18 to 24 year range Typically they're looking at a co-signer usually a parent Um, and there's some pretty easy ways to go about that But if they don't have a long credit history, maybe their credit history is only a year old And they do have some savings Simply a co-signer on that loan will get them into that home We can work it out on the legal side with an attorney so that everyone's interest is protected And if there's a default on the loan or that person can't end up paying that it defaults back over to the parent and Everybody's happy in the end So definitely ways to go about that Is that common to have a co-signer? I know they're it's common on a vehicle But is it common on a home where you're talking about a 30 year mortgage? The most people I've ever had involved in one home transaction was eight So yes, it can happen when you say eight. What does that mean? There were eight co-signers eight separate people on one transaction What? Do I have eight friends it would co-sign for me? I think there's something I'd like to buy. Oh my goodness Yeah, again, it just depends on the situation and who's involved in credit Who's got credit and who doesn't and how it's structured if it's going You know into one person's name in this case. There was a trust that was set up Um, lots of different fund options, but yes somebody getting a home at 20 years old very very doable Yeah Yeah, so good for you 20 year old one to to start building wealth through real estate That's well and I love the question because there are a lot of house cleaners That will wait year after year after year thinking one day I'll buy a house and like you said They're saving up for five years or whatever it is They're a great uncle told them that they needed And they're that has not become a reality for them just because there are some nuances and some unanswered questions One of the unanswered questions we had that came in through one of the facebook groups was about the closing costs And what are the closing costs and about how much of the home price are you expected to pay for the closing costs? And is that money that needs to be saved in advance? Or does that come out of the actual purchase price of the house and is that rolled into the price of the loan? There are loans that you can finance the closing cost and with the loan um And very often a seller Not so much in a competitive market, but um very often a seller will contribute Well, yeah, maybe even in a competitive market. I've seen a good bit of that lately where um a buyer will pay at or above Ask price, but then have the seller pay some of their closing costs which which can happen um so four percent um Of the purchase price of va loan They don't va loan doesn't have closing costs. Um, they have a it doesn't have any at all It has a funding fee, which I think is um less than Around two percent of the loan amount But that can be financed into the into the purchase of the home into the price of the home so that you pay it You pay it monthly So even if you've got somebody who like you said they're put putting it off putting it off putting it off Or even if somebody who just doesn't feel ready to purchase a home now Like they just want to be in a rental market because they feel like I mean I stay in this area for a long time or I Just I don't want the responsibility of home ownership as a lot of people see it Still speak with a lender and a realtor and prepare yourself so that when you are ready um You're you you're in a position where you can make it happen And you don't start at that point preparing yourself financially to get in a position of home ownership Uh, Talia says uh, Talisa says I have a great credit score income is fine My rent is getting high and thinking about buying But I don't have a huge down payment.  Again, it's going to depend on what she qualifies for and what loan type is best Again, also depending on lifestyle Um, we just talked about USDA loans, you know under if you make under a certain income and you want to live in a rural place You can get into a home with basically nothing down very little closing cost Um, if you want to live right in the center of a city, it's going to be a little bit different Um, you know, it's it's just going to kind of depend on the loan type Um pretty average Um, you know for for a down payment and and closing costs on a home Um is going to be somewhere around three four percent of the purchase price of the home And so it's kind of an easy way to calculate Um, you know, if you're looking at a 200 400 million dollar home, you know Look at those percentages and it'll give you kind of a basic idea Um, the other option is is get with your realtor And the realtor can give you some what's called cash to close worksheets And they'll take um, they'll take homes in different price brackets. I do this for clients all of the time Um, let's say you want to purchase what would a home look like at 200 versus 400 000 Um, and so we can look at both of those and look at the closing costs And what would go into that in terms of loan and down payment and we do a little worksheet And now you know that if you purchased at 200 000, that's what you need to come to the table with versus 400 um, and so Pretty easy to do but yeah, if your credit is good Um, and by the way, if you're leasing or renting You're paying someone else's mortgage That's just the bottom line. You're investing into someone else's investment fund not your own It's just money that's going out every month. So you'd be better off Doing whatever you need to sacrifice now to get into a place even if it's not your ultimate dream home You'd be better to get into something right away start building equity in it And who knows maybe hang on to it and turn it into a rental later down the road Or turn around and sell it for a profit and get into something a little bit nicer But you're if you're leasing you're just throwing the money away. I mean Yeah, and and you get the tax benefits of homeownership too and and I'm seeing a lot of that first time home buyers are buying Below their means with the idea of maintaining that property as a rental property Down the road because there's just so many more options now for Airbnb's Charlotte's a pretty good area for Airbnb's. It's a you know, we've got sports teams and and I'm sure saying Tonya too So a lot of for some home buyers are having that goal in mind to keep this property as a lease property But there are also to help figure out Down payments there are loan calculators out there and another good tool for people to do is to They're calculators online to help you see what your interest rate would be at your current credit score And what it would be if you were to increase it or if it were to drop And that that that makes a difference too Again, it can change the the price point of the home that you're looking to buy based on your credit score so sometimes that could be a good motivator to Look at what you can do to help boost your credit score some Tell me a minute for uh Tell me a bit for a minute about the interest rate because you just brought that up And I know that the interest rates have just kind of gone up a little bit in my area And I'm curious to know is this a time that you hold off and you don't buy a house Or do you still buy a house because it's not that big of a deal or is it a big deal or what how does that work? I can jump into that if you'd like Yeah, when it comes to interest rates, we've we've just seen some really craziness in the market over the past recent years I think what a lot of people don't remember is the average interest rate was always right around six seven percent If not higher Most of the 80s and 90s it was higher And so if you look historically at what interest rates typically were I mean when when my parents purchased they were at 16 percent and that was normal Um rates have always been a lot higher You know purchasing right now I would say is is definitely a plus interest rates are projected to continue rising Um, and so I think we will see interest rates continue to rise over the next year either way And so if if you're looking at purchasing is is six and a half seven percent high Compared to the the last few years. Yes so if if you're already in a home and You've got a low interest rate. There's no need to refinance right now But if you are a new time or a first time home buyer or you need to move Definitely moving sooner than later is going to save you money There's and you can always refinance if the interest rates Get crazy low again, and it makes sense for you to do it down the road Then you can refinance to get that lower interest rate And when you say refinance for a business owner and I'm talking about a business owner That's fairly new in the industry. They have two or three years business background behind them Is it possible to refinance or then do you run a whole regular role where they're like? Ah, you just bought a house your credit because we we gave you x amount of loan now you can't refinance like how does that work? Typical whole times about 12 months But then it also needs to make sense right? If if the rates have dropped and it makes sense to refinance then yeah You would pull the trigger on that but most loan companies are going to have you hold it for at least 12 months at the current rate Before there's any changes in that mortgage got it. Yeah, and it does need to make sense It needs to be enough of a of a rate change To make sense for you to do that I know one of the questions that a lot of house cleaners have is the debt to income ratio Can you guys explain this to me a little bit so that I know as a cleaning business owner? What i'm looking at as far as getting a loan Based on knowing that maybe I have some debt or maybe I have expenses I've got payroll. I've got money going out. I've got company cars What are they looking at? Yeah, well the I think the rule of so you've got front end and back end And your front end is is what you pay for your living expenses your your mortgage with your property taxes your insurance And I think the rule of thumb on that is 28% then there's the back end of your debt to income 28% of your Debt to income So 28% Of what you make should be attributed to your debt 36% is That would include Any other debt that you have Not things like utilities or cell phones, but any credit card debt you have Or any other loans that you're paying Revolving credit that sort of thing so Most I think 45% is what lenders less than 45% of Debt to income ratio is kind of the benchmark for lenders and So they're going to be understanding that you have a business and that you have some expenses And you probably have a student loan and you probably have a couple things like that And they're still probably going to try to help you get into a house if it's at all possible, right? I'm guessing that they're in the business to make loans Right and the whole and the whole goal is to encourage generational wealth through home ownership that the home ownership is is A backbone of our country And it's it's it's good for everybody so to educate people to get them on the right path to get there And erin said earlier if you talk with one of these specialized lenders and They know your situation then they can work with that so There are products out there where you can have higher debt to income ratio if you have offsetting situations So it's just finding that right lender who can understand your business your specific finances and find that product for you So those are general rules of thumb, but um I But but working with the right lender can help you navigate that Speaking of lender, uh, she loan says can you tell me why Wells Fargo sold home loans to another company? This was shocking What do you guys know about that and is it really shocking or is it that just matter of business for them? Really really simple answer is They bundled them up and sell them as a commodity on the stock market exchange Oh And they're they're up into different classes of assets And hundreds of those will make up a bundle and those are large companies that are traded usually on the Nasdaq So it's just matter of business. It's not really shocking at all. It's a matter, of course Yeah, I'm not shocking at all very often you'll get you'll get your loan and And then when it's time to make your first payment you're paying it to somebody different Yeah, I know that with uh youtube for example Like they'll bundle up all the ads and they sell the ads the same way And so it's not just like selling one specific ad, but it's a whole bundle of ads You know So I think a lot of businesses do that that way and they bundle it together and say this makes the most sense for us and off you go Nice Typically there's management companies that will manage and and run that you will pay into that for years But the reality is those bundles sometimes can change multiple times a day ownership They move a lot and so those those bundles are sold often But usually same management company holds it for a while usually several several years While that's trading hands So one of the questions that I have is about the documents that are needed in order to go through the process So let's say that I'm a cleaning business owner. I'm pulling together all my documents I've gone through the the Google I've picked out my realtor or it's one of my five neighbors the civil term And now I'm getting ready to pick my realtor. What documents are you guys going to look at or what do you need from me as a business owner In order to put the best foot forward and to give you Um un apologetic information so that we can just be honest and authentic and upright about the income that I'm not hiding That I am reporting and all that stuff Do you want to take that one brock or you're not you're not going to show very much of your Financial history to your realtor. You're going to work with your lender on that They're the experts in the field and we we As Aaron said earlier, you know We have that consultation to to find out what it is that you're looking for and for us to try and help Put you in touch with the right lender And and that may that you know the lender may change course before The the transaction comes to a close You know finding the right lender to work with you, but um in broad strokes generally You're going to want your tax information for the past two years Pay stubs Your income verification as a what is what is income verification? Is that your pay stubs? Yeah bank statements pay stubs You know if you're putting some money down They're going to want to see that those funds have been in your account for some time The reason for that is they don't want you borrowing money to put it in there to make it look like you can afford this But you really can't so they're going to do you know a little bit of a deep dive into your bank statements to make sure that those funds have Have have been in your account and Then they're going to look at things like child support if you are receiving or if you're paying child support Any supplemental income that you have Any loans that you have they're going to want to determine What your debt to income is then as a business owner, you know, then that's a little more specialized you're going to You're going to have bank statements and your assets and you may want to use your 401k towards a down payment If that's appropriate for the loan product and bring that information And this is all done Um Aaron mentioned the underwriting process that um that can be done before you go look at a home or as part of your due diligence process and so once you um Work with a lender and they verify the kind of loan product that's going to be most appropriate for you Then they put that loan in underwriting and those underwriters will look and and reach out to you for the verification that they need but Anything that you can think of that's going to prove Your income and your sustainability for the past couple years But but that's going to be something you work with with the lender and not your realtor So if you have a really great credit score, but your spouse does not can you purchase the house without your spouse being on the Lean or whatever and just have just just buy it all on your own Or do they consider couples that one has bad credit and debt and the other one doesn't How does that work in texas? Um either or can purchase Um, but you'll both end up being on the purchase agreement if you're married Okay more than five years in the state of texas Okay, in north carolina it can one can purchase but it takes two to sell So you can buy the home But if you go to sell it and you're married then both parties have to agree to sell it um and if if You purchase it together then the That they'll take the median of your credit scores. So if yours is 600 And his is 400 then it's going to be 500 so you may want to Self if you if you've got the income and all of that Yeah, or get or get that other credit score up Well, uh Aaron mentioned something that was interesting before where he said a home was put into a trust Would it make more sense to have a trust and maybe make let your business pay for it and keep your Husband or your wife out of it if that's the case and it was going to drop the credit score to the point Where the interest rates will go up or you won't be able to afford the home at all It could Again, we're talking about a very different thing there that then becomes an investment You're looking at about 30 down So a lot a lot higher down payment and that's structured a little bit differently Where that could be a good business asset It's it's a different structure. And so In in a case where somebody's looking at a first time home buying situation That probably would not be the best route for reasons because you're coming to the table with a lot more cash and so Again, it would it would have to work depending on the situation and then last thing on that note You know as far as documents to bring make sure you're either current with your taxes Or you have a payment plan to pay them off Because oftentimes we run into that too where we get into the process and they're like, oh, I haven't paid taxes in five years Don't be that person Thank you for that. That's awesome Maria Cristina says is it safe to buy a home that you just barely qualify for with nothing left for savings or unseen expenses If the mortgage makes your budget very tight, is it still worth buying? I love that question Here is what I would say What is your risk tolerance and where are you at in your life? If you're young if you've got a good job if you feel comfortable with the risk and you think you can do it Um, ultimately we as realtors want to help you do what's best for you in your life As a rule of thumb, I would say purchase a home at a lower price Don't max your budget out if you're qualifying for that, you know syntax or linar home at 250 Um, then go purchase a pre-owned at 180 And don't put yourself in that position where if the ac goes out You know, you're eating ramen noodles and and trying to sleep in a basement to stay cool you know, right and And you're you know, you can have tax increases too and Yeah And inflation and the price of everything else going up But like Aaron said, you could be a point in your life where you're going to have You're going to rent out two of the three bedrooms that you just bought and that will help You cover that mortgage You know, if you've got young children That's probably not going to be an option for you but if you're On your own and you've got two spare bedrooms and you can rent those out Then it may make sense for you to do that if you can supplement your income But you just have to the The prices of everything else they're they're not going down And you could see an increase in in your taxes and an increase in your Car insurance and in gag your car is going to break down or the hVAC is going to go out So that was great advice your risk tolerance. That's a great way to put it And I I promise you this as a homeowner a lot of stuff goes out A lot of stuff but it's out. We've had our house at about 13 years and I don't know why but it's like you're 13 like on the money stuff started busting, you know, like the air conditioner went out and then like the The nail pop started happening.  You know what I mean? Not going to happen Or or texas or yeah or texas. Yeah You gotta pull me up the money I would encourage everybody if you're looking to buy a home to try and you have an emergency fund Six months a year if you can do it So that when you are in the home, um, those things happen Then you've got that emergency fund. I think that um, the the rule of thumb is 35% of what you make if you can have that and save it for your emergency fund pay your debt down with 25% of it Have 10% of it for for fund money and then like your needs your car payment your house payment 30% of that but try and have money in the bank for those things Have an emergency fund Going into home ownership And there are a few things that you know You could always do to try to mitigate some of those expenses a home warranties Things like that. Yeah and getting with the right company if your ac did go out Yeah, you might be paying five six hundred dollars a year for that warranty And a 75 80 service call fee, but then they'll come out and actually fix those things and so If you have a good realtor, they'll lead you down the road of Your situation best worst-case scenario and you know those factors to look out for to Whatever your risk tolerance is, you know You want to save that 500 hours, but maybe that ac costs 10 grand You know the one in so a great point Yeah, we have time for one more question and margie robert says if I have one investment property What percentage will lenders look at towards my income? And then in order to buy another property Oh, I love this brooks. Do you want to take this one or do you want to I don't know that? Oh A lender is going to look at that as an asset Producing income and so what you're going to be showing is what's called the t12 or the trailing 12 What has that produced over the last 12 months? What is your mortgage on that investment property and what is your profit margin? And let's say you're making 200 a month profit on that Then as opposed to a liability What the lender is going to do is they're going to say well Can you get a lease in place for at least the next 12 months? So that that's money we can count on as income for you And now instead of This investment property being a big liability on your shoulders It's an asset that's producing and you can say hey, I've got them under contract for the next 24 months. Woo-hoo This is uh, this is the percentage. It's going to raise every year and this is my profit on it And uh, and they'll help you get into another home Now I know I know that one of the the reasons that this question is important is I know that a lot of house cleaning Business owners are trying not to put all their eggs in one basket And so looking at maybe a piece of property as an investment so that they don't have all of their income Just tied up in the business itself. Is this uh, is this and i'm just wrapping up today Is this something that you would recommend? Uh cleaning business owner do as soon as possible or would you recommend that they They wait a little bit until their business is more established before they go ahead and they branch out and try to invest in real estate I would invest as quickly as possible into real estate. I die hard into real estate. So that's what I would recommend Um the more you can invest into real estate and have those assets over time We've got a gentleman who is uh part of our brokerage. He's now on his tenth rental investment property His goal is to try to pick one up every other year And that's exactly what he does Um, and it's it's just keeping that investment rolling Um, sometimes it's taking a home equity line out of credit to get the next one But again, are they producing? Is it an asset or a liability on your books? And um, do you have those rental agreements in place where it can show that hey We're solid on this one for the next year over the next two years Is where it's really going to make all the difference. Yes get into real estate as quickly as possible. Don't wait Um and purchase lower than you think That you would like to live so you're not house poor And then if you think about long term, you know buying and holding Maybe every other year you you move into something a little bit better And keep that other one as an asset and lease it out Yeah, this was awesome Real estate's something you're going to be able to leverage for your lifetime. Yeah, so Oh, I love this. Thank you guys so much for joining me here today brook. Tell everybody where they can go to find you I'm at brook Bryant and um, I'm in charlotte, north carolina So if you're looking to buy or sell property in the area Be happy to talk with you and um help you achieve your dreams And they can find you at brook at ask brook brian at ask brook brian Awesome, and you can also find me on all the social medias at ask angela brown. Aaron. How about you? I'm at ask Aaron brown We'll keep it simple and i'm out of central texas and cover the greater area Again, we as realtors have a good network across the states So reach out to us anywhere you are and we'll help you get with the right person Awesome. Thank you guys so much for joining us today. This was so much fun And we'll meet again same time same place next week and we will answer more of your questions Until then have a great week and like Aaron said buy What did you say buy low and buy underneath your comfort zone below your means below your means Thanks again


Hello, my name is Louise and today is our open day here at the University of Greenwich Midway campus. Open day is a great way to come and see the university, see more of our facilities, meet staff and students and find out why our university is the best fit for you. So once you arrive on campus you need to head into our beautiful building and straight to one of our check-in desk, where these lovely ladies can give you one lanyard and an open day guide which contains a map of the campus and a timetable of all the activities that's happening today. Also take the opportunity to head into the main building where you'll see lots of schools run by the staff and academics. It's a great opportunity to speak to program leaders and find out more about the course that you're interested in. We'll have plenty of schools, accommodation, student finance, admissions and help with anything that you may have concerns of and start from your university degree. Here at the other faculty of engineering science have lots of different facilities, labs, electronics, different things to entice you no matter what your interest in studying here at the University of Greenwich. Our drill hall library is the longest library in Europe. In here they run lots of events and dropping sessions to help with all of your academic work including help with finding books or references. Lastly don't forget to visit the deep end, it's our student social hub where you can eat, drink, play games and make friends.


White always has those eyes up, tried to pocket feet at the holiday, and Murray got his hands in there. And White takes it right back, throws it up, JP. Derrick White is locked in right now. What a play from Derrick White. Winning play after winning play.


Hey, welcome back to Tai Chi Top 5 Techniques. We're going to do Technique number 3, Rise and Fall. Hey, are you ready for Technique number 2, the most powerful Tai Chi technique? Here we go, it's called Rise and Fall. Here's how you do it. We're going to bring our hands up and bring our hands down. Very simple. If you do it with the proper Tai Chi techniques and Tai Chi Qigong, you get tremendous power from this very simple yet deceptively powerful technique. From the side, now notice that my whole body is moving throughout the whole movement. If I exaggerate it, it's going to be like this. That's a little bit more exaggeration. Now if you want to do it in a more internal fashion, you won't see any of that. One point to notice is that when I'm raising up, I'm squeezing the inside of my legs. When I'm coming down, I'm expanding my knees outwards. If I keep going, it's going to go down and my knees will keep going outwards.  Up your spine into your hands and then it comes down. It goes back down to your Tan Tan and do your Hui Yin or Perinium and then splits off to the outside of your leg down to the feet into your K-1 spot. All that is acupuncture stuff that you don't really need to know. All you need to know is that you need to use your whole body and have it move up and down very smoothly. Now you know the technique, let's show you how to use it.  You don't walk around the street ready to fight people, right? How do you walk down the street?  So let's say a tag comes out of nowhere. It comes out of nowhere. I see something. Whoa! That's your natural reaction. Your hands just come up naturally. That's the first rise. Rise. Which opens me up for the fall. Boom. Right down the eyes. Scrape the face. Depending on how dangerous the attack is, then you want to up your force.  Then you're going to go to jail or you're going to get in big trouble. But if it's a guy, he's got a knife, he's got a weapon, he's got friends with him, then it's okay to gouge the guy's eyes out. So you have to be aware of your situation and be tactical about it. So here you go. Rise. Fall. Down. In training, just do it on the chest. That's enough. Just pretend that's his face. That's not comfortable even for the chest. No, not at all. And you can even do it with one hand. Let's say you're holding a baby or groceries like that. You have one and you still do it with one hand. So another one is a reverse. Fall and rise. Let's say that rise and then another one's here. Fall. Rise again. So you can just use this up and down motion to do a lot of deflection. Down. Up. Down. Up. Boom. Another way you can use it, let's say that you're shorter than a guy, he's really tall. Boom. Up this way. It's a little bit too high, but you can just do it as you're short and he's coming for you. Duck. Boom. Okay, very simple. And if you practice enough, you can really do some serious damage to your arms right now.  You've got tough bones, but for a regular guy, what do you think? Yeah, it's definitely got quite the sting for sure. It shocks the whole body basically. I can feel it radiating already. Okay, and I'm not using any power. That's it. It's being relaxed. Very relaxed power. So the key of this is to use relaxed power, use the whip. See how I'm using my body to whip it? With my whole body. So it's not just my hand going up like down, like in robics. They keep your, they move their hands in straight lines like this. Actually it's moving in a whip. Matching this is the whip. Boom. Okay. And when it's coming down, it's also a whip. Boom. Like that. Okay, so use that whipping action. Boom, right in the temple.  Boom, in the temple, in the ear. Okay, that can definitely... What do you think? Definitely, man. Definitely. You can't pass the date in person. Alright, so use with discretion. In training, just tap it on the head, or on the chest. Okay, or just do it on the arm. The arms can take the hits because they're strong, right? Okay, or shoulders. Okay? Alright, so that's rise and fall. Hey, thanks for watching top 5 Tai Chi Techniques. You want to watch the next video, just click on the video box here or you can check out some of my other playlists. If you haven't already, make sure you subscribe to my channel and click the button right here. So I'll see you in the next video.


Welcome to lecture 28 on measure and integration. If you recall, we had started looking at the computation of product measure of a set E in the product sigma algebra and we had shown this can be computed via the sections of the set E, integrating the sections and taking the measures. So, let us recall this result and then we will continue to generalize this result for functions which are non-negative and integrable functions. So, let us recall the result that we had proved last time, namely if x a mu and y b nu are 2 sigma finite measure spaces and the product sigma algebra, a product space is x cross y, a times b and mu cross nu is a product measure space, then we showed that for any set E in the product sigma algebra, the measure mu cross nu of E can be computed by either taking the section of the set E at a point x and that gives as a subset of the set y and we showed that this is in the sigma algebra, you can take the measure of this section. So, this becomes the function of the variable x and then you can integrate out this function with respect to mu to get the product measure or equivalently you can take the y section of the set E that gives a subset of x which is a measurable set and then you can take the measure of mu measure of that that gives a function of y and then integrate out that with respect to y to get the measure of the set E. This result we want to re-interpret as follows. See the measure of the set E x can be written as the integral of the indicator function of the set E with respect to the product measure. So, the mu cross nu of the set E is nothing but the integral of the indicator function of the set E on one hand. On the other hand, if you look at the x section or the y sections, they are nothing but the indicator functions of the set E again. So, when you take the integration with respect to y that means you are fixing x. So, you are looking at the section of E at x. So, nu of E x is nothing but the integral over y of the indicator function of E with respect to the variable y and similarly the other variable. As we had mentioned, the importance of this result lies in the fact that the indicator function of a set E is a function of two variables and to find its integral with respect to the product measure, what we can do is we can fix one of the variables say x. This becomes a function of one variable y and one shows that this is integrable with respect to nu. So, when you integrate out with respect to nu, the variable y is a function of x, which again can be integrated with respect to mu and this integration gives you the integral of the indicator function of E. So, the important thing is that here when you are integrating with respect to y, the variable x is fixed. So, this is only a function of the variable y. So, for every x fix, you treat it as a function of the variable y, integrate that out and then integrate out that integral with respect to the other variable and similarly we can interchange x and y and get the result. So, what we want to show is today is that this result is true for all non-negative measurable functions on the product space x cross y. So, the theorem we want to prove is the following. Namely, if f is a function on the product space x cross y and it is a non-negative function which is. So, f is a non-negative measurable function on x cross y is measurable with respect to the product sigma algebra. Then, the following statement is sold namely if we fix one of the variables say x. So, if x naught is fixed, then consider the function f of x comma y naught and similarly y goes to f of x naught y. So, for the function f of x y, either you fix the variable y at y 0 or you fix the variable x at x 0 and treat it as a function of one variables only, then these functions are measurable on x and y respectively. So, what we are saying is that for a function of two variables, if it is measurable with respect to the product sigma algebra, then fixing either of the variables gives you a function of the one variable which is measurable on the corresponding basis with respect to the corresponding sigma algebras. These are non-negative functions. So, you can integrate them out. So, if you integrate this function x going to f of x y naught with respect to x mu, then that gives you a function which depends on y. So, the function y going to integral over x of f x y d mu x. So, you integrate it out the variable x, this gives you a function of y and similarly you integrate out f x y with respect to the variable y, you get a function with respect to x. So, the claim is these two are well defined non-negative measurable functions on their respective spaces. Finally, these are non-negative measurable. So, you can integrate them out with respect to the corresponding variables. So, if you integrate out them, so first integrate with respect to y and then with respect to x that is same as integrating first with respect to x and then with respect to y and both are equal to the integral of the function f of x y with respect to the product sigma algebra. So, this gives an extension of the earlier result and so it says that for non-negative measurable functions, if you want to integrate with respect to the product sigma algebra, product measure, then you can do it one variable at a time. So, these integrals, these two integrals are called the iterated integrals. So, the claim is that for a non-negative measurable function, the integral with respect to the product measure is equal to the two iterated integrals. Once again the importance being you are integrating one variable at a time. So, let us prove this result. So, this proof is going to be built up step by step and this is what I call as the simple function technique. So, the idea is that when f is the indicator function of a set, this result is true by the earlier result on product measures and then by looking at because everything involves integrals. So, an integration being a linear operation will get that from that this result is true for non-negative simple measurable functions and once it is true for non-negative simple measurable functions, an application of monotone convergence theorem will give us that the result is true for all non-negative measurable functions on the product space. So, that is the approach basically we are going to follow and this is what I call as the simple function technique. When you want to prove something for non-negative measurable functions on a measure space, verify it for the indicator functions, verify it for the non-negative simple measurable functions and then verify it for the limits of non-negative simple measurable functions. So, let us prove this. So, the step one is that the required claim holds when f is the indicator function of a product indicator function of a set E in the product sigma algebra. So, let us look at that. That was what we have already shown. When E is so step one, when E is an element in the product sigma algebra, we had already shown that the product measure mu cross nu of E on one hand is equal to you take the indicator function of E and integrate out with respect to x d mu and then integrate out that with respect to the variable y, so d nu. That is same as you first integrate out the indicator function x y with respect to d nu. That means keeping the variable x fix, you are integrating with respect to y and then compute the integral of that with respect to the variable x. So, these two are equal and the middle thing, if you recall, we said it is equal to the indicator function, integral of the indicator function of E with respect to the product sigma algebra. So, this is besides this saying that the claim holds for f equal to the indicator function of a set E, E belonging to the product sigma algebra. So, this is step one and now from here we want to go to step two. So, step two is let us take a function. So, step two, the required claim holds for non-negative simple measurable functions. For s f equal to s, a non-negative simple measurable function on x cross y. So, let us take, so what does the function look like? So, a non-negative simple function s on the product space looks like sigma A i indicator function of some sets E i, where i is 1 to n and these E i's are sets in the product sigma algebra A times B and their union of E i's they are pairwise disjoint and their union is equal to x cross y. Now, by step one, what does step one say? Step one says for each E i the claim holds. So, step one says for every i equal to 1, 2 and so on n, the integral of the indicator function of E i with respect to d mu cross nu on one hand it is equal to the integral over x, integral over y of indicator function E x y d nu and d mu and also equal to the integral over y, integral over x of the indicator function of E d mu and then d nu. So, this is what we know. Now, let us just observe, because this is true for every i and integration is linear. So, that means if I multiply, I can multiply throughout by A i. So, if I multiply by A i, so I can multiply here by A i, so this is E i. So, if I multiply, so this is A i and I can multiply by A i and I can multiply here by A i and then take the summation, so some over i, then summation over i, summation over i and here will be summation over i. Now, this summation integration will be linear, I can take the summation inside. So, when I take this summation inside the integral and then again take it inside, I will get summation of A i times indicator function of E i, integration with respect to nu and then integral with respect to mu is equal to this I take it inside, that will be summation of A i. So, let us just write that, this is more of writing than understanding. So, when I do this summation and take the summations inside, I will get integral over x, integral over y of summation i equal to 1 to n A i, indicator function of E i d nu d mu is equal to, so that is equal to and this summation inside will give me integral over x cross y of summation A i, indicator function of E i d mu cross nu and the last one will give me integral over y, integral over x of summation i 1 to n A i, indicator function of E i d mu d nu. So, this is just using the property that for every indicator function of a set, the result is true and integration is linear. So, the result is true for finite linear combinations of these things also. So, this gives us and this is precisely my function s. So, this says integral over x, integral over y of s x y d nu d mu is equal to the integral over the product space. So, this is the function s, so s of x y d mu cross nu and that is also equal to the other iterated integral, integral over y, integral over x of s x y d mu of x d nu over, we have already done it. This is over y, so over y that should be nu actually and this should be mu, sorry, because this was over x, so that should be, no that was d mu and this is d nu. So, this is over x, so d mu and d nu, so that is, so this says that the result holds, so this proves the second step namely the claim holds for f a non-negative simple measurable function. So, now from here to go to general non-negative functions, step 3 says we should be able to prove the result when f is, so let us take f on x cross y to r star, f non-negative f a times measurable with respect to the product sigma algebra. Now, we look at the characterization of non-negative measurable functions, f being non-negative measurable implies that there exists a sequence S n of non-negative simple measurable functions S n of x increasing to f of, S n of x y increasing to f of x y for every x y belonging to the product z x cross y. So, that is by, because of the fact that this is by the, so this is by the fact that for every non-negative measurable function there is a sequence of non-negative simple measurable functions converging to it. Now, by step 2, so by step 2 we know that for every S n the corresponding result holds, so what does it mean? That means for every S n the integral of the non-negative function S n x y d mu cross nu x y is equal to the iterated integral, so let us write say for example, integral over x, integral over y S n of x y d nu d mu and similarly the other iterated integral. Now, what we are going to do is observe the fact that for every S n this result is true and S n is a non-negative sequence of non-negative simple measurable functions increasing to f. So, by the definition of the integral this one converges to the integral of f x y d mu cross nu of x y. So, this is by the fact of monotone convergence, this is not really monotone convergence theorem, this is actually the definition of the integral. So, if f is a non-negative measurable function then its integral is defined as the limit of any sequence of non-negative simple measurable functions increasing to it. So, that is by the definition. On the other hand we will compute this integral and so it is the corresponding iterated integral of the function f. So, let us look at this integral. So, integral over x, integral over y S n of x y d nu d mu. So, this we want to show claim that this converges to integral over x integral over y of f x y d nu d mu. So, this is what we want to show and once that is shown, so on one end this converges, so this converges to this iterated integral on the other end this converges to this integral of f. So, these two will be equal and we will be through. So, let us try to prove that this iterated integral converges to this iterated integral. So, for that let us observe first that S n, so note, so here are the steps for proving this. So, first of all let us try to prove that integral over y with respect to nu converges to corresponding integral. So, for that let us note that S n of x y is increasing to f of x y for every x and y. So, if we fix x, then we get a function y going to S n of x y for every y belonging to y and because S n itself is increasing, so this sequence of functions we already know these are measurable functions. These are measurable functions for every simple function. We had seen that if we fix one of the variables, the other one is a measurable function for simple functions that is true. First of all this is clear. Therefore, fix x, this is an increasing sequence of non-negative functions. So, this is a sequence of increasing sequence of non-negative functions and each one of them is a measurable function on y. Second observation is that each one of them, so the function y going to S n of x y is a measurable function. That is in a sense obvious because, so to see this we note that so for this, so observation is, so let us say S n, so let S n be equal to something. So, sigma, let us say it is a i n indicator function of e i n for some i equal to 1 to some indexings at 1 to m n. Then for every fixed x, so for x fixed, y going to the indicator function of e i n x y is measurable, so that we have already observed that that is a measurable function while computing the product measure we saw that this is. So, each one of them is measurable with respect to the product sigma algebra because it is an indicator function of a set and for every fixed x, this will be a measurable function on y. So, that will be the sections, so that will be the measurable, scalar multiple of a measurable function is measurable and the sum of measurable functions is measurable. So, this is obvious fact that for a simple measurable function S n, if we fix one of the variables in the other variable, it becomes a measurable function. So, this is a measurable function. So, that means for x fixed, so what we have got on is for x fixed, the sequence S n x y over n is a sequence of non-negative b measurable functions on y and also it is increasing. In fact, it increases to, so what does it function? It increases because S n increases to f. So, when we fix one of the variables x, this is going to increase to the function f of x y, x fixed as a function of y. So, increases to the function y going to f of x y. So, it is a perfect setting for application of monotone convergence theorem. So, by monotone convergence theorem, we get the following. So, by monotone convergence theorem, we get, so to this applied monotone convergence theorem. So, by monotone convergence theorem, the integrals S n x y d nu y over n y limit of that must be equal to integral of f x y with respect to d nu y. So, this is what we get. Of course, for every x fixed, so for every x fixed, we get that this limit must be equal to this. So, that means what? That means this function, so this is a function of x. So, that implies that if I look at x going to y f of x y d nu y, if we treat this as a function of x, then it is a limit of these functions, limit of non-negative simple integrals of non-negative simple functions. So, that means that this function is measurable. So, that implies, so this implies that this function is non-negative measurable. It is a non-negative measurable function and this is a non-negative measurable function and it is a limit of this sequence of non-negative measurable functions. So, by star, I can apply again another application of, again another application of monotone convergence theorem. So, this limit of, this on the left hand side, the limit of integrals of S n with respect to nu that also is a limit of measurable function. So, this itself is a measurable function with respect to x and because S n's are increasing, these integrals are also increasing. So, this is, so if we call, so this limit is equal to this. So, now what we are saying is another application of monotone convergence theorem to the fact that if we look at the sequence of measurable functions, this is a measurable function. So, integral of that, so let us write, so the function x going to this is a non-negative measurable function. So, what is left to be proved? We want to integrate this with respect to mu. Now, so that is what we are saying that to this we apply monotone convergence theorem. So, we will get the limit of these functions is this function. So, integral limit of the integrals, so this says limit n going to infinity, integrals of this function, so integral over x of these functions, these functions are S n x y d nu y d mu x. So, this limit of this must be equal to integral of this with respect to x again by monotone convergence theorem. So, let us write that, so this is equal to integral over x, integral over y of S n x y d nu y d mu x. So, this limit is equal to this, but on the other hand we had seen that on the other hand we had seen that this iterated integral for S n's that is equal to the double integral. So, this is one thing upon observation also. Let us look at the other fact, so what is the other fact? So, also we have that integral over x, integral over y S n x y d nu y d mu x. For simple non-negative simple measurable functions the claim holds. That means this is equal to the double integral, the integral over x cross y of S n x y with respect to the product measure mu cross nu. So, this is because we have already proved in step 2 that the result holds for non-negative simple measurable functions. And now if I look at, so this result is equal to this, so limit of this must be equal to limit of that. So, implies the limit n going to infinity of this left hand side must be equal to limit n going to infinity of the right hand side. So, this one and that is coming here, but limit of the left hand side we have already seen is equal to the limit of the left hand side. We have already seen it is equal to this and what is the limit of the right hand side? S n is a sequence, so we have already seen that S n is a sequence of non-negative simple functions increasing to f. So, this must be equal to integral x cross y of f x y d mu cross nu. So, that proves that this must be equal to this. So, that proves that the step 3 proves that the integral of f x y with respect to integral of, let us just see how we proved that. So, what we have shown is this limit must be equal to this and what was that limit of that quantity? So, what we have shown is that integral of d mu cross nu is equal to over x cross y is equal to limit n going to infinity of integral over x, integral over y of S n x y d nu y d mu x. So, this is what we have proved just now that this limit on one hand side was this, other hand side was this. So, limit of these two quantities must be equal. So, this is what we have proved, but this quantity, let us see what is this? So, note that S n for every y fix was increasing. So, let us look at the sequence for every x fix that is an increasing sequence of non-negative measurable functions increasing to the function f of x y. So, monotone convergence theorem says this inner integral converges to integral of y f of x y d nu y. That is what we had already observed and then again this is a sequence of non-negative simple non-negative measurable functions. The application of monotone convergence theorem gives us that integral of this limit of that must be equal to d mu of x. So, that says that the double integral of the non-negative simple function is equal to the iterated integral of the non-negative measurable function iterated first with respect to nu and then with respect to mu. We can interchange x and y. So, same arguments you will imply. Let us say that this is also equal to integral over y, integral over x of f of x y d nu y d mu x. So, basically let us just go through the ideas in the proof that basically this proof is an application of the fact that integral for a non-negative simple function is built from the limits of integrals of non-negative simple measurable functions. So, that fact is used very effectively because we know that the corresponding result is true for indicator functions and integration is linear. So, that allows us to say that from the indicator functions you can go to non-negative simple measurable functions by just taking scalar multiplications and additions of characteristic functions. So, that will give us that the result is true for non-negative simple measurable functions. And then just some suitable applications of monotone convergence theorem will give us that the integral of a non-negative measurable function on the product space can be computed via the iterated integrals. Let us just go through this proof through the slides once again so that we have a clear idea what we are doing. So, the step one that the required claim holds when f is the indicator function of e that is the previous theorem that we have proved. And step two the required claim holds when f is a non-negative simple measurable function. So, from step one to step two one goes via the fact that integrals are linear operations. And then one goes to step three that the required claim holds when f is a non-negative measurable function. So, that requires applications of basically applications of monotone convergence theorem. So, step three is the crucial one where lot of applications of monotone convergence theorem are used. So, let us just go through that again. So, let S n be a sequence of non-negative simple measurable functions such that S n increases to f. So, that is by the fact that f is a non-negative measurable function. So, now let us fix x. So, then the sequence S n x is fixed. So, in the variable y is a sequence of non-negative simple measurable functions on y and it increases to the function f of x y for x fix. So, point wise S n x dot as a S x fix S n x as a function of y increases to the function f x as a function of y. So, an application of monotone convergence theorem is not required here. So, this is a limit of increasing sequence of measurable functions. So, that says that the function y going to f of x y is a non-negative measurable function because this function is a limit of measurable function. So, first fact to being used is that limits of measurable functions is a measurable function. Now, we can also apply monotone convergence theorem to conclude that the iterated integral of S n must come converge to the iterated integral of f with respect to y. So, that is the first application of monotone convergence theorem that for the non-negative measurable function f for the variable x fix its integral with respect to the variable y is well defined because this is a non-negative measurable function and it is equal to limit with respect to n of the non-negative the iterated integral of the non-negative simple measurable functions S n with respect to y. Now, this result also says that this equality also says that this the right hand side treated as a function of x. So, that means that converges to this integral and by the fact that the required result holds for non-negative simple measurable functions this function integral of S n with respect to y is a measurable function of x. So, here we were using the step 2. So, this is a sequence of measurable functions converging to a function. So, that means this integral must be a measurable function. So, again limits of measurable functions are measurable.  So, the iterated integral of f with respect to y is a measurable function with respect to x and it is non-negative and once again this is a non-negative function and is a limit of these integrals limits of this measurable functions. So, another monotone convergence theorem application gives that integral of the iterated integral of the integral of S n with respect to y its integral with respect to x must come to the corresponding integral of f with respect to x. So, here we are applying monotone convergence theorem that the integral of x integral of integral over x of the integral of f with respect to y must come must be limit of the corresponding integrals with respect to the non-negative simple functions. Now, come back and for non-negative simple functions we know the result is true. So, this iterated integral must be equal to the double integral. So, that says so this is equal to the double integral and now S n is a sequence of non-negative measurable functions on the product space. So, this again by either you can say application of monotone convergence theorem or just by the definition this limit must be. So, this is equal to this and the limit of that must be equal to the integral of the function f over x cross y. So, that says the corresponding result holds. So, this iterated integral of f is equal to the double integral of f with respect to mu cross mu and similarly the other thing can be proved you can interchange the variables x and y. So, this result is true. So, this is the result which is called Fubini's theorem 1 which says so this is the first Fubini's theorem which says that for a non-negative measurable function on the product space if you want to integrate find its integral with respect to the product measure you can do it by integrating one variable at a time. Either you can fix x integrate out with respect to y and then integrate with respect to x or interchange choice is yours you can first integrate with respect to x and then with respect to y. So, the two iterated integrals for a function of two variables is equal to the double integral for non-negative measurable functions. So, this is called first Fubini's theorem which helps one to integrate functions of two variables. So, next we want to show that this result also holds for functions which are integrable. So, we want to prove that for a integrable function the corresponding result holds. .. So, let us look at the proof of that. So, let us look at so let us take a function F which is L1 on x cross y it is integrable with respect to x cross y and we want to say that that the integral of F x y over x cross y d mu cross nu we want to say that this integral on one hand is equal to you can integrate first x y with respect to nu we want to claim this with respect to y over y and then integrate out with respect to x d mu x or one should be able to say that this is also equal to you take the function F x y integrate out the variable with respect to mu so x and then integrate out with respect to y d nu of y we want to say that these two this results hold. Now, for that on obvious if these equations are to hold where F is not necessarily non negative so that means what first of all the inner integral for example integral of F x y with respect to y must exist that means we should be able to say for a function of two variables which is integrable when I fix the variable x as a function of y that is integrable so that is integrable and then that gives us a function of x and then we should be able to say that is integrable with respect to x and finally these two are equal and similarly the other result must hold. So, the theorem which we want to prove is the following namely that is called Feminist theorem 2. So, namely if F is a integrable function F is a integrable so we want to prove the following that if F is a integrable function then the following statements are true namely one that for the function of two variables if I fix either of the variable then with respect to other variable it is integrable not for all but we are able to say that the function x going to F x y and y going to F x y for the other variables are integrable for almost all y and for almost all x. So, for almost all fixing of coordinate the other variable it becomes a function which is integrable with respect to the other one. So, that is one and then secondly once these are integrable you can integrate out. So, it says that the function y going to integral of F over x with respect to mu and similarly the integral of y F with respect to y these two are defined almost everywhere and of course they are defined almost everywhere and are integrable and hence the third step says they are integrable and indeed the integrals the iterative integrals are equal to the double integral. So, we would like to prove this theorem. So, to prove this let us proceed as follows. So, we are given that the function F belongs to L 1 of x cross y. Let us write the positive and the negative parts of the function. So, F is equal to F plus the positive part minus the negative part and the integral of F x y with respect to the product measure mu cross mu is equal to integral of the double integral of F plus with respect to the product measure minus the integral of the negative part d mu cross mu over x cross y. So, that is the definition of the integral. If F is integrable then the integral of the function is nothing but the integral of the positive part minus the integral of the negative part of the function. .. Now, let us look at them separately. So, F plus x y of course d mu cross mu over x cross y. So, F plus is a non-negative function is a non-negative measurable function. So, by the result fubinous theorem 1, I can write this as integral over x integral over y F plus x y integral over F x y d mu with respect to y and then d mu with respect to x. So, implies by Fubinous theorem 1 that is Fubinous theorem for non-negative measurable functions that integral of a non-negative measurable function can be computed by iterated integrals. So, this is n also equal to let us write the other one also. You can interchange integral over x F plus of x y d mu x and d mu of y. So, this is for F plus we have used the Fubinous theorem 1. .. Now, let us observe F being integrable this quantity is finite. So, all these integrals are finite quantities. So, that means, all these being finite implies. So, for example, the first one implies. So, implies because of integrability that integral over x integral over y F plus x y of d of mu y d mu x is finite. Now, here is an important observation that we have earlier proved that if the integral of a function is finite, then the function must be finite. So, here we are using integral finite implies function finite almost everywhere. So, this we had already proved. So, this fact we are going to use now. So, look at this inner this integral with respect to mu of this function is finite. So, that implies that the function. So, this as a function of x, x going to integral over y of F plus x y d mu y is finite almost everywhere, almost everywhere with respect to x. So, we have used the fact that integrable function implies that the function is finite almost everywhere. Now, once again for almost all x, this is finite. That means, so this also implies that the function. So, y going to F plus x y is finite almost everywhere and of course, integrable, because this integral is finite almost everywhere. So, it is a function which is integrable and finite almost everywhere. So, implies I can integrate it out and this is a non-negative function. It is integrable and non-negative integrable function. So, we have for this already seen this is equal to. So, that we have already seen that for non-negative integrable function, this is equal to this integral. Similarly, the function x going to, similarly the function for x going to F plus x y is finite almost everywhere and integrable is also. And the corresponding results also hold for, similar results holds for F minus. So, that means what? So, all those four functions, so all the four functions are finite and integrable. So, we can integrate them out and we have the results corresponding results for, so these are all integrable. So, that is the first part. So, that is the first part that these functions are integrable almost everywhere and correspondingly almost everywhere with respect to x and y and these functions are also defined and are integrable. So, that means we have the following. So, they are all integrable and finite and for F plus x y with respect to x cross y d mu cross nu, we have got this is equal to the iterated integral with respect to x with respect to y of F plus x y d nu d mu. Similarly for the negative part, we have x y d mu cross nu x cross y is equal to integral over y integral over x of F minus x y d nu d mu. So, now we can and all these are finite quantities because F plus and everything is integrable. So, these are all finite quantities. This is finite and this is finite. So, I can take the difference of the two. So, the difference of the left hand side, so subtract second from the first and use the fact that integrals are linear. So, the difference subtract implies subtraction and similarly and also the corresponding identities for the other one interchanged thing. So, this is also equal to integral over y integral over x of F plus d nu d mu for non-negative that is true. So, we will subtract this from this. So, we will get integral of F d mu cross nu x cross y because integral of F plus minus integral of F minus is integral of F is equal to the iterated integral of F plus with respect to x y minus the iterated integral of F minus with respect to the same iterated integral. So, that will give you y integral of respect to x of F plus minus F minus. So, that is F x y d nu d mu. So, that will prove that for the integrable function the double integral is equal to the iterated integral one of them. The other proof is similar. So, basically this result that for integrable functions the corresponding interchange of integrals hold is basically coming from the previous result namely that the corresponding result holds for non-negative simple non-negative measurable functions. So, what we have proved is two Fumini's theorems Fumini's theorem one and Fumini's theorem two. Fumini's theorem one says that for non-negative measurable functions the double integral the integral over the product space can be computed by integrating one variable at a time and similarly this can also be done for functions which are integrable. So, we will continue this Fumini's theorem a bit more and then specialize it to for integrals for R 2, R 3 and so on. Thank you.