from the American Creativity Association on Think Tech Hawaii. I'm your host, Phyllis Bleece. Today on the show, we'll be discussing the topic of unity through creativity, not through force. With creator, innovator, artist, and educator, Ms. Lori Marshall, you can send questions by email to questionsatthinktechhawaii.com. Welcome, Lori. Let me start with you and tell us something about this title. What does it mean unity through creativity, not through force? Unity through creativity is a goal. It is a practice. It is something that works in the world where all of us come together as respected peers and share ideas to make a world that works for all. Unity through creativity is a nonprofit that I founded in 2001 and it's been going for 20 years. And with witnessing every day the bombardment of Ukraine, the contrast between the world I know is possible, where everyone is respected and everyone's gifts are asked to be shared and celebrated. It's so different than the unwanted physical destruction that is going on in Ukraine and in so many places in the world. It is a peace building through art, practice, and it is inspired by nature. It sounds like getting to nature is something we're getting very far away from with the idea of pushing the button on nuclear warfare. Yes. I'm wondering, you know, our tagline today is about the healing, the trauma of war in Ukraine. I know you've done it in Sarajevo. You're doing it with your project in Afghanistan and Cyprus and Uganda today is including Ukraine. Tell us what your project is to heal the trauma of war. And how is it creative? I'd like to share the first slide if you would be so kind to do that. The singing tree project is a collaborative mural project that envisions success. And it envisions the healing of heartbreak. And this painting that you're seeing is the same painting that is behind my back. And it was created right as COVID hit and it's called the singing tree of embracing our unknown. And we were a group of women who are being trained to be facilitators of the singing tree project were all facing the trauma of COVID. We were in India, England, of Somalian heritage in the United States. And we each came up with looking at what is breaking our heartbreak. And then twisting that around into what we can do about our heartbreak. And one of the things we can always do about our heartbreak is to express it. And to turn trauma into beauty and purpose into pain. So we turn the pain of COVID into the image that you see behind me. If you go to the next slide, I'm going to show you how we heal trauma. And without me on it, because it has very important words. These words are by Sherry Mitchell, who is from the Pennott Scott tribe. And she is a lawyer and a visionary educator. And this is the basis of how we heal trauma. And as she wrote, if we hope to create a new reality, a new reality, a new reality being presented and focus on the reality that we wish to create. And this is so important because we can't heal unless we envision the possibility of healing. And we at Unity to creativity use art and storytelling and dance and music to create the village that allows people to express their trauma. So let's go to the next image. And again, pop it up. So what you're looking at here is the Ukrainian singing tree of strength and freedom. This is the study for it. And in the center is a tree with a nightingale, which is Ukraine's national bird. It's a viburnum tree. And we put the tree rooted into the heart of the world, because I think we're experiencing this heartbreak of how crazy war is. The leaves have come from young people around the country from Ohio. And people are sending leaves in from England, from all over the United States, from Uganda. And we are taking this moment to collectively express our love for Ukraine. And that's what we're trying to do. And that's what we're trying to do. That's what we're trying to do. That's what we're trying to train. And trauma cannot be healed without love. And again, unity through creativity, not through force, means that we lead with love. And that's so hard. It is so hard. Lori, let me ask you a question. You said, how large is this project going to be? How many people are participating around the world right now in sending in these leaves? And how, how many people could work on this singing tree project in Ukraine right now? Can people in the United States and around the world, can they, are they sending in drawings of the leaves? Yes.  So these just came from England today. Oh, yes. From an elementary school in England that we have a relationship with that just completed the singing tree. Of inclusion and protection. So I don't know how long, how big it's going to be. We're starting off with an eight foot by four foot sheet. Students at University of Texas in El Paso are taking my design and putting it on this board of eight foot by four foot and we'll get in as many leaves as we get in. Everybody's welcome if we need to make another, another mural that'll be great. And I'd like to share the origin of the singing tree project because I think you'll understand how organic it is. In 1999, I made a mural with elementary school in Leesburg, Virginia. And all the kids in the school made helped to paint the mural and a eight year old girl named Meredith Miller said, I wish the whole world could see our mural and then the whole world would be happy. And then she said, what if the whole world made a painting together and that vision of a child changed my life. And it brought me to the place of wanting to invite the whole world to create together instead of to destroy each other. We have Meredith on the screen. And there's Meredith and she's all grown up now. And right after Meredith gave me that remarkable earth and soul shattering vision, somebody gave me the book, the singing tree. And Michael, if you could go to the next slide. The singing tree is a book by Kate Serity, which feels even more relevant now with the terrible destruction in Europe. Her daddy was a soldier, a Hungarian soldier, and fought Russian soldiers. And one night his battalion crawled on their bellies all night long to escape the enemy. And everything had been destroyed by war, just like in Aleppo and in the Ukraine now. And they, when the dawn came, one tree had survived. And in that tree were birds who aren't normally together. And they were singing a song that had never been heard before. And we can choose to destroy our planet, which is like the singing tree of the galaxy. And we can choose to destroy each other, or we can choose to create beauty that's never been seen before. And that's how the singing tree project began. And there's 105 murals made by 52 people from 52 countries. And over 21,000 people have contributed. And I'd love to share a video of two years of singing trees. They are intergenerational projects, but they are often student led. Because in order for there to be peace building, we have to train young people and listen to them.  It just working with the colors would make your sadness, you know, just in your interiority. Yes. What are some of the reactions of the people in the room working on it? Do you have a whole range? Do they cry? Well, I mean, if you didn't take in this project to that building in Ukraine last week, that was bombed where they were living down in the basement. I mean, wouldn't this be something that they could have been doing together? It's very humbling because in the, in the face of bombs being dropped. Art seems like a humble response. And yet when you make a mark and make, you're making a decision. And when you make a decision and take action, it releases all kinds of positive hormones in our brain and in our body. And the fact that in war, you feel so helpless. It then making doing art together, doing music together, telling the story. It empowers people to, to say what their inner experience is and be witnessed. And the, we can be witnesses to what's going on. And yes, I've had people cry. Yes. I mostly have people have joy at what's possible. And I remember a kid in high school who was speaking, he was a red net kid was looked at a leaf that a kid who was called a hippie kid made. And the red net kid said, I didn't know that he had that in him. And to see the inner beauty that we all come with. Is so very important. Yeah. Great question. Now you've already had the Sarajevo singing tree project and Sarajevo went through horrendous internal strife. Yes. And so you have a little perspective on this. What are the comments you're getting now? What kind of changes this form of creativity make in the lives of the people engaging in it? That's a beautiful question. When I made the Sarajevo singing tree with young people whose parents have been killing each other in the nineties. We, we did this in 2014. To celebrate a hundred years anniversary of World War one. And there was a peace conference there. The students didn't want to put any continents on the earth. So the structure of the singing tree is a tree on the earth and space and everyone envisions solutions to community challenges. As I said before, when the kids from Sarajevo made the earth, they put musical notes around it. They put no continents, no borders. They, they saw themselves as being tied through their creativity, not through I'm a Bosnian, I'm a Serbian, I'm a Croatian. So it allows people long term to understand that everyone is a creative being and to have more respect for their own creativity as well as for that of others. And I think you have some more examples to show us that you've worked with. I really want to give the viewers an opportunity to see all the different methodologies and ways and participations that they can be part of. And I think you have a process for training people in this project and in this process, right? So maybe sharing a little bit about that and where they can find the tools for doing that as you take us a little bit more around the world. Sure. Would you be so kind of show the next slide, please. So this is the image of the singing tree being the, the galaxy of the, the earth being the singing tree of the galaxy. And this image was envisioned by a seven year old, the blood dragon singing tree to prevent extinction. And the young people that are coming in now have incredible insight about the precariousness of our time. And we are training people to, to become singing tree facilitators so that this image all around the world can be seen as a symbol of, we can work together. We can regenerate. We can create peace. And there is abundance. And we listen to the children and we value the wellbeing of children. So that's why I love having intergenerational design teams. And the, you can go to unity, unity through creativity.org, and you will see the certification information there. And could you go to the next slide, please. And while he's doing that, we have a question from the audience. He's asked if he says, if you speak, you speak of getting perspective when a creative idea pops up. Do creative ideas come in the form of images? Do you literally see your creative idea? Absolutely. And I welcome everybody to draw their ideas. So these, many of these singing trees are designed with input from 35 or 50 people who draw their image of how they see. The solution to the issue of water or the heartbreak of autism or the heartbreak of addiction. And I ask everyone to draw and guess what? Everyone has unique, beautiful images to draw. I've had one person in all the 25,000 people I've worked with, not make a successful unique image. And that was a person at NASA who walked out of the training. Everyone else has a unique image. We've been drawing for 60,000 years or more. And we've been told that only a few people can draw. But if you can draw the alphabet and make a straight line or a curved line, there's nothing you can't draw. So yes, seeing the image is available to everyone without vision that people perish. It's there in us. And if you're doing a joint project, you could ask you or someone else say, this is what's in my mind. Could you just sketch that out for me? And you co-create your future, your image. And you write, we welcome writing as well. And we are very inspired by Harriet Tubman who saw every one of the people that she took on the Underground Railroad as already free. And I see a world where everyone is contributing their gifts and is acknowledged and lives in peace. And that's, that's what the whole world's invited to create. And I think we're going to be able to do that. And would you be so kind to share the next slide? So this is the water willow singing tree. That was made by teenagers. And I love how the young people understand the connection between the human life and the life of nature. With the umbilical cord running around the master tree. And the leaves are water drops. And you know, we are broadcasting out of the Hawaiian islands. And any deeply embedded water imagery certainly is something that, that Hawaiians can relate to.  And it, it's, it's lovely to see this. It would be nice to start a singing tree project around the indigenous connections and cultures and interweavings of all the indigenous cultures. Just not the Hawaiians and the native Hawaiians. And, but every one of the cultures that came to the islands and they're now one very large group of multicultural. Yes. People. So maybe you could talk to us a little bit about the indigenous people's work that you've done. Yes. I had the privilege of working with res refuge, which is in Fort Defiance, Arizona with a DNA youth. And they worked three years on a singing tree. To honor native tradition and they made the earth a Navajo basket. And it's on the unity through creativity website. There's a gallery there and you can just type in, um, a DNA singing tree and it'll pop up. And if you go to the next site, the next slide, you'll see the name of the tree. And you'll see the name of the tree. And there, this is a singing tree that we made to honor. All federally registered native tribes in the United States. And it was designed by Mary and Hansen, who is a Kiowa. Artist. And every leaf has written on it. The name of one of the federally registered tribes. And. It's rooted in nature. It's rooted in the mutualism and cooperation of nature. The stories of survival of the city. Fittest, which is what is going on in Ukraine is a, a small part of the story of life on the planet. The competition lives within incredible collaboration. And the trees. And the trees. And the trees. Give us two of seeds and nuts and oxygen and clean the water and sink the CO2. If you go to the next slide, you'll see how. Before we leave, before we leave, I did want to point out. I know that there's a Hawaiian leaf in there. I don't know which one it was the monkey pod tree. Or the high biscuits tree. Or what, which. Which everyone that they use. So they used the same tree in the morning. But it's more used to be on one of those leaves because it believes are actually similar. Yes. Right. They're all the willow leaves. Yes. And this is the logo for the singing tree that's going on. And Uganda. That we've just begun. singing tree logo. So you can see the tree itself is the leaf of Ukraine because the people in Uganda that we're serving are in a refugee settlement camp and so we're honoring that all of the refugees on the planet are united. And if you go to the next slide, I know we have just a few minutes left. These are some of the books that I've made to support nurturing creativity and young people. The Flood of Kindness is a story by my godson who was eight years old and wrote a story about Hurricane Katrina. It's for children about being creative in the face of natural disasters. Reading the Oz now is for educators and parents and the singing trees is the story of the first five singing trees that were made. So I thank you so much for being here and having me share this vision that unity through creativity is possible and practical and beautiful. Well thank you. We didn't get to the yin book that your sister wrote and I can tell let the audience know we'll stay tuned and we'll have you back. Maybe we could start a singing tree project through Think Tech Hawaii and American Creativity Association. It's just been such a delight and let me sign off now with leaving it right there and letting our audience know that you have been watching the creative life on Think Tech Hawaii. Today we have been discussing the topic of unity through creativity, not through force with creator, innovator, artist and educator Ms. Lori Marshall who leaves us with a creative singing tree artwork approach to healing division and even the most worn torn areas of our globe. Mahalo for participating Lori and Mahalo to our viewers for tuning in. I'm Phyllis Bleece. We will be back in two weeks for another edition of the creative life. Aloha.


Try this. What's up, Money Geeks? Mr. V here. Welcome to another video, guys. So in today's video, I wanna share with you guys one key strategy that I use for trading. This is a strategy that I kinda like, look at the stocks there. Something's gonna happen to them, and then I go in and create a watch list to trade these stocks. So it's a strategy that I've been using to make a lot of money in the markets. I wanted to share that with you guys, but before we get started, if you're new to the channel, I want to talk about how to earn money, how to save money, how to invest and build wealth. So if that's something that interests you, go ahead and hit that subscribe button and any notification bell so you don't miss out on new content. So the strategy that I wanna share with you guys when it comes to investing or when it comes to trading is using what they call the earnings report. So if you've heard about earnings report for companies, this is where companies give out sort of like a state of the union of the company every quarter. So our first quarter, second quarter, third quarter, fourth quarter companies will come out and give that sort of a state of the union. And based on what those companies, the information those companies provide, you would see the stock of that company would either really get pumped up or you see it get beat down. So a lot of companies usually come out and give information and us traders are sitting there waiting for that information to determine how we wanna do it. And some people might even sell and get out of certain positions for certain companies and then wait to buy the bottom if they anticipate that the earnings report they're really gonna suck. And then, and so that is a strategy that I've been using a lot. And if you guys have been following like some of the posts that I have either on YouTube post or on my Facebook group, if you're not part of that Facebook group there's a link in the description, you can join it at post, this earnings report there every week before the week starts. So I put them like Sunday evening I'll just put them in that group so people can go check the companies out and see which one works for them. So basically for me, I do print out the earnings report.  So I print out this sheet. And so here's the strategy that I use. Once I print out the sheet here just in case you wanna know where I get this one from. If you go to the website called Earnings Whispers they provide you a holistic list of all the companies that have their earnings that particular week. So you go to have a calendar, you can click on the calendar, pick a specific date. It will show you all the earnings for that day and you show you what they call pre-market earnings and after hours earnings. So you can decide which ones you wanna trade. So I take the list, let's say on Monday I'll create a watch list in my Weibo account because that's what I use for trading. I'll create a watch list and I will look at the companies and I will go in and do detailed analysis of the companies. If I see that this is a company that is really getting impacted by COVID in a negative way. It's impacting sales or impacting their business. Then I will probably move that company and put it under my list of shuttables in my watch list of shuttables. And then if the company that is thriving let's say like Zoom and all these other peloton like these companies that are what I call COVID companies that are benefiting from the COVID and I'll put them under loan which means that their earnings report will probably come out on the positive side. So a good example I'll give you guys is like Pinterest. When Pinterest had their earnings report the stock gap almost $30 a share.  So if you had done your homework you'd anticipated that Pinterest earnings report was coming out and you know for sure that Pinterest is benefiting tremendously from COVID because a lot of people are studying business as people are posting and doing that stuff and running ads on Pinterest. So they're making good money.  And then you take other companies that are not doing so hot when their earnings come out the stock would tank. One exception that I've seen like even this past last month or so when Tesla had their earnings report the earnings report the numbers were just fabulous. I mean like every dream of a company the numbers were just so good but yet Tesla took a beating. I still don't know how to explain that and it always happens with Tesla. So that company that you can short in that case you short it and make money. So when I see a company that I know for sure that are gonna get impacted that sales are gonna be really down. Then I can even short that upfront. Or if I see that as a COVID company their sales are gonna be really good because they're benefiting from people staying at home. And I think that it's gonna gap once their earnings report comes out. What I would do is I can buy some position in that particular company and hold it into their earnings. But it's usually a risky business because sometimes when your earnings come out you see the stock would gap down and then before like shoot up in order for the earnings to come it would shoot up and then start gapping down. So you have to be really smart to be there to look the directions. And if you bought in and it gaps go up you take profit and then you can reverse the trade and sell again up there and actually follow it down and make money in both directions. So that is a strategy that I wanna share with you guys and see if that's something that you people are using. Again, the website that I use to get a list of all the companies that have their earnings every week is called Earnings Whisperers. I'm gonna put that in the description. So we'll check out the company, it's free. It's not, you don't need to subscribe to get it. So just go to, or you can follow me either here on YouTube and check out my post or you can actually join our Facebook group. I'm gonna start posting them on my Instagram account as well. So I mean it's information that I want you guys to benefit from. So I'm gonna put it out there and just see if he helps anybody. Let me know in the comment section, have you traded using earnings report? If yes, what your experience does hesitate to share that in the comment section. And also if you're looking to get started with investing, like I mentioned, I do use the Weibo platform for my day trading. And right now, Weibo is doing a promotion where they're giving out four free stocks, not one, not two, not three, four free stocks. If you sign up and deposit a hundred dollars. And also if you just want to test and see what it's like to day trade, it's an excellent platform. They have what you call paper trading feature where you can go in there, they give you fake money to trade it. You can test it really during market hours and test and see how trading actually works. And that is a really good way for you to get comfortable before you jump into the ocean with the shacks.


So we're gonna talk about see people always ask what is your day like Tom owning a business and we'll start with Corey's here Because you guys are going to do a camera job over at a company way down in luna pier Yeah, it's not an hour. Well you drive slow. He actually does. He's not he doesn't speed at all You're Steve first. Yeah, so we're loading up the truck for that job We're gonna do a video because we're gonna now that the summer is here We're gonna have Corey clean his truck out and we'll do We'll do a video right now with things may fall a little bit if you open this door But we'll do a video of what's in our truck someone asked about all the cabling equipment and everything else I would love to go down there and film it but like Corey said, it's about a 45 minute drive And I actually have a lot of other work to do So other things that I do when I come in well, I was actually already here I just am greeting I usually get here early and then I greet all these guys here And I complain when you're late, I generally post a meme If you could start here at 10 a.m. That would be great or whatever time you're supposed to be here Cory was here on time today. So well, I was here early. So I don't have to say anything about that Marv is over there Marv are talking about what it's like to work here in a typical day This is not a typical day. Oh Marvin has his badge on I was I was at a chamber event this morning with puppies There was puppies. Yeah, that's the important part to think about here big big white fluffy guy It was some kind of poodle something. He's so cute his name was brand I want to something And this is what reason we like the chamber sometimes they have a vet where puppies are the steve's going hold on.  I mean we got all together. We bought like 50 of them in the last week or so But this particular plus 14 and 29 and yeah, so we bought quite a few of them And that's what's going in for the dynamic job and in the studio I haven't been able to do videos last few days because we've been so busy I did an interview this morning. That's gonna be part of a new podcast. It's coming up I can't tell you the details. You won't find out for another week and then I'll be promoting it Then you'll find out. So we have these projects in here These are the next batch of them getting programmed for another one. We sold this table has been covered last night How many speakers did you have set up in here? 16 plus another eight.  So all the speakers were in here And if you want the speakers are for that big job that we talked about the project called revved up fun Um that project that I done a couple videos on we're on the man lifts There's we're also doing all the speakers because if you can pull the cable for cat Uh cat network cable you can go ahead and pull all the speaker where at the same time So we did matter of fact we were doing the amplifiers and everything We're already got rack mounted amps. So this that project is actually going a little bit beyond the scope of what you may expect from Normal it but it's something else that we do So coordinating all that project and then finding out that the speaker was damaged. Good news is For four but the best news is the client changed the scope You know as we've talked about that happens and we don't need them so we can send them back So it doesn't even matter so that's there But this is also inhibiting me from doing some of the videos because I can't do much with this table right now I've been trying to eat I made some food and it's getting cold because all these other things keep popping up And the other problem we have is let me go over here Is all these boxes are everywhere now all this is staging for projects and All these are the mounts racks and everything that we stage here. We set everything up We build like the if you've seen my little photo from the Uh video we call the spider unified camera setup We stage everything set it up build it break it back down and do it that we Once we go in and mount them we never worry about will they work everything's been pretested preconfigured And to the point of even labeled ahead of time of where it goes with naming and everything That makes it really simple. Uh mara's been doing a sales thing and that's kind of why we're busy So he goes out and does all the sales and confirms that Somewhere in between a couple things got missed. I won't lie that happens And we're missing these little uh knob adapters So we got to sort that out. Those are things that sometimes roll uphill of oops. I forgot something So that's been going on. Uh the other things I did was we ported over our phone number We're gonna talk about that on vlog Thursday because now the full Thing is set up and my favorite part of the day though is the fact that the back doors open Because we've been letting the breeze flow through and it also goes back to what I was eating It turns out when you cook cabbage, uh the staff gets upset because they're like tom you're eating healthy But it stinks. So they thought that there was a sewer leak. Is that what that was? Is it? Yes, that was cabbage. It was still residual. I was like what is going on in here? That's terrible. Yeah, so this is kind of what a day looks like. I get up a lot I don't always get a chance to do my computer. I run around do this to the interview I got more phone calls to make us interrupts I come in and interrupt them a lot because I come out of my office and it's usually because I go Hey, did this get done that get done did this get done Uh, there's something to be said as much as I am a techie guy For still that human interaction level of aggravating Marvin. I mean, I could just send him a message So good at it. It's not near the satisfaction I'm coming over here and saying Marvin let's talk about that project So that's all right. I'm sure I do my fair amount of annoying tom as well with hey, remember how you were supposed to do that thing You didn't do that thing. We're not going to talk about that thing that tom probably didn't do Yeah, so now because I'm losing steve and cori to that onsite job. It's going to be me Kyle and marve here We got another guy come in any afternoon. So help sort this out. Oh, oh no, you know, we have another guy Most of the time we have another guy most of the time. I don't keep track of these things These guys because I I have to put layers in between or everything if I get involved in everything I'm an anti micromanager. So I was like that's why I didn't even know that guy was not coming in today I don't even do the payroll here by case anyone's wondering. I don't because I would screw it up I really love like two weeks ago What do I pay you? I don't know. Let me find out I had to ask that because I didn't I don't look I outsource all my accounting and I set the rates So I'm like, I think you need to raise because he's been doing really good with all this web work and everything Which is what he's doing right now. And uh, so I say you need to raise But I don't know how much I pay you and I and I feel like calling my accountant. So I just asked him No, he gets a raise People think too seriously about business. I mean, we are a Functioning working normally less chaotic company who's been in business for 15 years. We're doing well Finances are pretty good. And uh, but there's still things like people. I loved it. I think the most real Business talk I've seen sometimes has been from, uh, Sir Richard Branson read his books by the way if you haven't very entertaining and uh, light hard to look at business But related to that one of the things he said was he always gets mixed up at the difference between net and gross profits He said that in an interview and I'm gonna start laughing. He's like, but I'm serious I'm dyslexic and he's joking around about it too. He says it makes for interesting board meetings And that's one of those things that being a business owner isn't about like, oh Do you know exactly how many dollars and pennies right in your bank account each little detail? Those are actually not the details that matters much It matters that I make sure everyone has stuff to do make sure there's processes that are documented everyone's supposed to follow Um, and that's kind of how the mix-up happened Someone was out of parts on something and that's when I have to as a business owner stop and look at the process going Okay, they were out a red mark was made in an order sheet for the job But somehow the next step didn't happen Usually it does but apparently everyone's out of them and this is actually part of what happened with some of the unified cameras If you don't know, uh, they're in demand. We actually have people calling us for them We don't sell them directly but they wanted to buy our inventory because So many places were out of stock on a couple of different things unified makes some great stuff We really like their product and I think other people seem to like it as well Which is why it's so didn't man So I just wanted to give you a little walk through because I was like just This is all the stuff that kind of goes on sometimes It's not always chaos, but in the morning getting all the jobs ready making sure everything and it's just me Making sure the big picture stuff. I don't want to know the details. I want to know big picture What day is that job getting delivered? Is there anything else we need to change about it? Make sure you know processes were followed and then I look at it as a process not as a well someone in order part No, what process can we put in place to make that park it ordered? That's the Business process thinking that you do But that's a lot of what my job is here because I do some of the sales But marvin does a lot more of the sales to me. So he's going to the networking events He's going to that but if you are the salesperson and not the geek I'm much more the geek than the sales guy Then you would be the one as a business owner, which is frequently true They're the ones that may go to the sales meetings all depends on process But marvin once again has a process That I gave him to follow in terms of you know get the sales get the clients An enlightening moment for the business owner is when I asked kyle and steve yesterday. I'm like That plumbing company where'd they come from? It seems like oh, yeah, they're onboarded managed and everything I'm like cool. I met them on facebook. They said we'd like to have managed services I passed it off to the team and then just showed up in a dashboard like they're onboarded There have been envoys they're got recurring invoices like everything's done And I did nothing more than call that person and like they said they want managed services That's process though. That's what that's the important thing to focus on as a business owner Processes and look for gaps in those processes or if things keep rolling up to you That's when you know there's a gap and you have to rethink the process again To make it work But that's what I wanted to share with you that is a little bit of my day and a little bit of the chaos That I have this isn't a morning It kind of calms down and trends down on the afternoon I did manage because I got here so early today. A lot of times my day starts here at the office at about 6 30 am Yeah, I got a few other things done But the uh, I'll get a video done or something like that But then this is this is what everyone gets here. So I just grabbed the camera I'm I'll share with you guys a little bit of actually what goes on. All right. Thanks Thanks for watching if you like this video Go ahead and give us a thumbs up if you have some feedback leave it in the comments below If you'd like to subscribe to our channel hit that subscribe button Hit the bell icon to let youtube know you'd like to know about new releases on videos You can also find new releases on our website laurance systems comm slash blog where every video automatically gets posted So you can always find our videos whether youtube notified you or not Also, if you like to hire us for consulting services, go ahead and hit laurance systems.com fill out the contact form Tell us about the project you would like us to help you with we work with a lot of businesses We work with a lot of other it people who need services done Also, if you want to help the channel out in other ways, we have a patreon We have right below me a amazon store where you can check out some of the products We've reviewed and as many of them as available on amazon You can also check out the things we love and that's an ever-evolving list of discount codes offer codes a different software and affiliates You can find that on our website as well or just follow it in the link below right to the things We love landing page including the hot sauces. We recommend which is always changing. All right Once again, thank you for watching and see you in the next video


Hello, this is a video about linear regression or correlation performing a hypothesis test. A sample of 20 children was asked to draw a nickel. The diameter of each nickel was recorded as well as each child's family income. Incomes and thousands of dollars and a nickel and nickel diameters are given in the table. Test the claim of significant correlation at the 0.05 significance level. So first thing we're going to start off with is we're going to state our hypotheses here. So for any hypothesis test that deals with correlation, the null hypothesis is always rho. This is our population correlation coefficient is equal to 0. And alternative hypothesis is rho is not equal to 0. What this top hypothesis is saying there is no correlation and what this alternative hypothesis is saying is there is correlation, so keep that in mind. All right, let's calculate the correlation coefficient. And we do that using Google Sheets. You do not want to do it by hand. So in Google Sheets, we'll go to the regression tab and we're going to clear out any data that's already there. And then we need to type in the data. Now you can either try to copy the data over from the actual question itself. If that doesn't work out very well, though, I recommend taking the homework question data, pasting it in the Excel. I do know for a fact that will work. And then copy the data over column by column. So depending on your computer, it may be a little bit more difficult to do this than you think. But if you paste it in Excel, move it over column by column. I know for a fact that it will work for you. All right, so let's copy over our second column, paste it into B2. Make sure you leave A1 and B1 as X and Y. Those are your header columns, your headings for your columns. All right, so it looks like our correlation coefficient, R, is negative 0.297. Negative 0.297, that is R. Now I need to find my critical value. The best way to find your critical value is by looking at your critical value table for linear correlation. So I had 20 pieces of data. And the degrees of freedom would be n minus 2 or 20 minus 2. So let me write that down real fast. For this type of test, degrees of freedom is n minus 2, 20 minus 2, which is 18. So in our critical value table, we just send the data down to 18. And lucky there we have 0.444, 0.444, 0.444, 0.444, 0.444, 0.444, 0.444, 0.444, 0.444, 0.444. Next. Now, anytime you conduct this hypothesis test for correlation, your null is always rho equals 0. There is no linear correlation. Or rho is not equal to 0 is the alternative hypothesis, meaning there is linear correlation. So you can use your p-value alpha method if the p-value is less than alpha, we reject H naught. Or you could compare the correlation coefficient to the critical value. Let's first do the p-value alpha method. Well, I know alpha is 0.05. Now the p-value is, let me give this to you in your Google Sheets. So it's not that hard to find. p-value is about 0.2035, 0.2035. And it's clear to me that the p-value is definitely greater than alpha. So since it's greater than alpha, we will fail to reject the null hypothesis. We'll see what happens when we compare the correlation coefficient, the absolute value of it to the critical value. Well, first off, the absolute value of the correlation coefficient is the absolute value of negative 0.297, which is positive 0.297. So what I want to do is I want to compare 0.297 to 0.444. All right, so I reject the null hypothesis if my correlation coefficient is greater than the critical value. In this case, though, it looks like we are less than the critical value, which means we cannot reject. We fail to reject H0. So regardless, you get the same result no matter what method you use. So fail to reject H0. So that means all eyes are pointing to the fact that there is no linear correlation in this case. So our claim was that there was linear correlation, which means that there is not sufficient evidence to support the claim in this case. Now let's find the regression equation for this data. You get y hat equals AX plus B. That is the general format for a linear regression equation. A and B are given to you in Google Sheets. A is about 24.69. B is about negative 0.06. So let's just fill that in. Y hat equals negative 0.06X plus 24.69. To predict what diameter a child would draw a nickel given a family income of $35,000, it would be appropriate to use what? So in other words, can I just plug in this income of $35,000 into the equation and figure out how big the child would draw the nickel? And the answer is there is no linear correlation based on our test we just conducted. So we cannot use the regression equations, the equation that we just found. We cannot use it because there is no linear correlation. There's no evidence for it. So you cannot use the equation to make predictions. Instead, the best estimate anytime linear correlation doesn't hold true is to use the mean y value. In this case, that would be the mean coin size. That would be the best estimate for how big a child would draw the diameter of a nickel given a family income of $35,000. So that's how you conduct a hypothesis test for linear correlation.


Poland says it's ready to respond appropriately to potential threats from Belarus. Poland is ready to respond appropriately to potential threats from Belarus. Polish Deputy Defence Minister Wojciech Skakowicz said, commenting on alleged violations of Warsaw's airspace by Belarusian military helicopters, the senior defence official said, we do realise who our enemy on the eastern border is. If such situations continue to take place and there is an escalation of tensions, then our actions will retaliate appropriately to the potential threats. Skakowicz called the situation with helicopters a provocation aimed at Poland and NATO. The senior defence official also noted that on August 1st, Warsaw's armed forces received instructions to deploy additional units and military helicopters on the eastern border. On August 1st, the Polish government said that two Belarusian helicopters had crossed over into Poland's airspace near BIO Wiecie. After that, the Polish Foreign Ministry summoned the Belarusian interim charge d'affaires in Warsaw. According to the Polish Defence Ministry, Poland duly informed NATO about the incident. Meanwhile, in Minsk, the Belarusian Defence Ministry characterised the Polish accusations that Belarusian Air Force MI-8 and MI-24 helicopters and air defence troops had violated the border as far-fetched. According to Minsk, the charges served merely as another pretext for the Polish leadership to ramp up the movement of military personnel and equipment to Poland's border zone with Belarus.


And now, for your U.S. Army Europe spotlight. One of the issues tackled during Exercise Allied Spirit 1 at Hohenfell's training area in Germany is how to get a multinational force to accomplish point-to-point secure communications with different systems and different nations. That's what a tactical voice bridge is for. But what if it doesn't work with all systems? The problem was that the American connector didn't fit on the Dutch radio, so we had to make a kind of adapter cable for connecting two radios together. So this is the first time this bridge has actually worked to our knowledge with a Allied nation from a U.S. radio. And this is what Allied Spirit is about, addressing the smaller but very real challenges in order to focus on the larger mission.


Some interesting things are developing in the world of the Nintendo Switch Pro, Next Gen Switch, Switch 2, whatever it's called, the supposedly 2021 Nintendo Switch device, which at this point there has been so much smoke there has to be fire. Everything is pointing to 2021. Some sources are even saying early 2021. And it might sound crazy to some people to talk about this in the midst of Nintendo having its best sales year ever for a Nintendo Switch, but Shantara Furukawa himself kinda sorta talked about the next Switch device, saying they are working on cutting edge technology and something that can get about 5-6 hours of battery life and you don't work on cutting edge technology and not start to get into talks about actual cutting edge technology. And now we have a new leak coming out of, well, out of Taiwan. Now, it's important when we talk about this, because Nintendo does have factories in Taiwan, they are the ones that actually make Nintendo Switches for the North America region, they split it off from China, they were trying to kinda circumvent some of the new tax laws that were going in place in the United States against China imports and goods by, you know, taking the parts that are manufactured in China and basically assembling them over in Taiwan for North America. Well, what's interesting here is the talk about the screen technology, because one of the early leaks that we had way back on the Wall Street Journal some two years ago was about how there was going to be new screen technology. And there's even a company Nintendo has partnered with that is in the screen technology space, although their screens have yet to appear in a Nintendo Switch or Switch Lite device. But now we have an idea of the direction Nintendo might be going with new screen technology. And this comes from Economic Daily News, which is a Taiwanese news outlet that is very accurate when it comes to leaking of products, not so accurate when it comes to leaking of release dates. So if they had a release date in this article, you can basically ignore it. But they are, you know, very accurate when it comes to leaking things from the manufacturing side in terms of what's actually going on. They have a long ranging history of this and Taiwanese made electronic devices. Alright, so what is happening here is that the console is apparently going to get a mini LED display from Inelux. That's the company that Nintendo is going to partner with to get this mini LED display out. Right now, they currently support they currently work with Sharp and JDI. But I'm, this is interesting. Mini LED technology is extremely interesting because some people said all they should go straight to OLED and all the shads. But let's talk about what mini LED actually is. So mini LED has nothing to do with the size of the screen, you can have mini LEDs in 75 inch TVs, let alone in smaller screen displays. But if you're unfamiliar with the technology, it's basically a main screen for the console that would have mini LED technology is using that as opposed to the traditional 720p LCD screen. So it's like a hybrid of current backlit LCD screens. But it has an OLED style local illumination and dimming. So each pixel in an OLED screen emits its own light and can be turned on and off individually. That's what makes OLED so great. But LCD screens rely on illumination from back lights which can result in light spill in dark areas of the screen that appear gray rather than black. This is why OLEDs have been considered king for a long time. However, in contrary to traditional LCD back lights, mini LED screens provide much more local feel the backlighting to illuminate the pixels on the screen more precisely. This improves screen contrast and potentially battery life because there's less waste or light spill as the light is only delivered to pixels that need it. Apple is actually going to be adopting this technology in future devices coming out in 2021 and beyond. Right now they do use OLED, but they're going to be switching from OLED to this because it's cheaper without hardly any loss in quality. Now OLED is still the king of display technologies, but obviously OLED has a really big caveat to it and that is screen burning. It's real. It's a thing. There are reduction things happening software-wise to try to prevent it from happening, but it's still an issue with OLEDs. But this isn't an issue with LCD and it's not an issue with micro LED either. So micro LED just to explain it one more time and maybe even more lame in terms is basically the same technology being used in LCD except LCD relies on either getting its light from the sides or getting its light from a big source in the middle and pushing out. Then what this does is it creates more light sources. So it puts little LEDs all around the screen allowing them to control each section of the TV. However many LEDs are in each section of that TV efficiently and power efficiently as well because when you're using an LCD, the whole screen is lit up at once whether the screen is black or not. This is often why even when you turn off the lights, if your TV is in some sort of sleep mode but is still on, you could tell the screen is on even when the lights are off because it doesn't look black, it looks gray. So you're still using energy in those sleep modes whereas that's not the case with mini LEDs. Mini LEDs, most people when they see a mini LED display next to an OLED display have a very hard time telling the difference and yeah it helps with HDR support and all that as well and supposedly mini LED tech is a kind of a emerging technology but it's rather cheap to make to be honest. It's not that cost expensive. It is more expensive than the traditional LCD but we're talking pennies on the dial are more expensive. It's not that expensive of a tech. It's not like going to OLED which is much more expensive or micro led which is just you know an even better OLED technology but also a lot more expensive. So obviously this is going to lead to obviously better contrast on future switches, better blacks, deeper blacks you're going to see better potential HDR support and yeah obviously this could lead to better resolutions and all that as well that looks crisper and cleaner and this would honestly be needed if Nintendo was ever planning to do any sort of 4k upscaling if they were going to use an upscaler of any type whether it's DLSS 2.0 or however Nintendo would handle that. It's important of course to have the screen technology in place that doesn't make it look like it's such a drastic difference looking on your switch to looking on your 4k TV. Obviously you don't want to be looking at a really low quality screen and then looking at your 4k TV which all of a sudden looks like the system is almost a completely different system because of the color differences so this will help alleviate a lot of that. In fact a lot of TVs that we get today feature mini LED for the LCD technology or they go to OLED a lot of the LCD traditional LCD is starting to kind of fade out even in the TV space outside of the cheapest of the cheap TVs of course which are just going to give you whatever they can get from the factories for next to nothing but yeah I'm this is obviously exciting news because it's another Nintendo switch pro leak slash rumor slash whatever you would like to call this coming out of the manufacturing space and it's it's just we are entering a period where I feel like all three platform holders are going to be launching new technology in the next six months after all we're like what a week and a half two weeks away from the you know Xbox Series X and S launching you know another couple days after that for the PlayStation 5 and then if you think we could be three or four months away from the switch pro or whatever they call it the new Nintendo switch the switch to it's possible even that it might be almost indistinguishable what a next-gen switch would look like versus this because you're not going to include this technology which creates all these better image quality features if you're not also going to include the technology inside the system to take advantage of those image quality features like if you're still going to have games running at 360p and being super blurry in handheld mode what's the point of a better quality screen if you're going to have a better more high quality screen you're obviously going to have the components inside to actually take advantage of that which means we should get more RAM and like faster RAM speeds faster bus speeds faster CPU speeds you know you know more VRAM like there's going to be clear advantages in the system and having a more powerful screen that is a little bit more power efficient is a big deal it leads to better battery life and yeah believe it or not it's kind of crazy how we could actually get a power increase while reducing power consumption like a power increase in through the performance but reduce power consumption because we're just so much better at manufacturing chips at smaller nanometers and all that today than we were back in 2015 this isn't always the case if you want the most power or power you need a beefy power supply like you know you want a 3090 for your computer you're going to need a pretty beefy power supply but we're not talking about computers we're talking about mobile here and I think that Nintendo is positioned extremely well with the switch pro to take advantage of the momentum of switch and just keep it going in the midst of these new console launches when they finally start to get in stock at some point next year and it's easy for everyone to pick up so yeah that's just me you guys let me know what you think about this down in the comments below I am going to be getting this platform whenever it comes Nintendo has already essentially confirmed it exists so now it's just a waiting game I want Nintendo thinks the best time is to release it obviously releasing it after the hype cycle has maybe faded from the new gen platforms might be a good idea you get clear the holidays get your switch sales out of the way then announce it next year and go from there anyways I am Nathan Robojans from Nintendo Prime I want to thank you so much for tuning in and I will catch you in the next video


What's up everybody, Jason here with jazzy's casebricks.com 2020 leave auto baseball one box for your ground and seems number four sold out Where we're giving away two icon random hit spots, which the break sells out with this break here. So there you go Joe Montana got pulled yesterday. That's kind of funny that we had to randomize that to everybody I'm sure we would but yeah guys college rules apply here. Of course since this is not a you know Trading card break like a baseball card break. These autographed baseballs will just have the players autograph on there So we'll go by college rules, which is teams that they're currently on if they're active in the MLB Or if they're not active or retired teams they play for the longest and again tie breakers by games I think Jack just mentioned that those of John Montana pulled yesterday. So if it's like a non baseball player Then of course that'll be randomized to the group But again, we first do the one box break Showcase the baseball and at the end of the break we're randomized 30 customer names top two names get a spot each in diamond icons So good luck. Let's do the break first Dishroll it and we got a two and a one three times one two three three times Justin Down to weed all right three times here one two three three times Royals down to the Mets Justin with the rose Douglas with the A's Ryan with the Brewers Wade with the Astros Douglas with the Mariners Wade with the Yankees Adam with the Blahatres Stephen K with the Blue Jays Ryan Herald Do you have the White Sox Richard Miller with the Dodgers Ryan Herald with the Twins Wade with the Braves Richard Miller with the um Marlins or sorry with the Reds Joe. Yeah the Marlins Jason K with the Rangers Ryan Herald with the Giants Oliver with the Rock his last one Roger Nicholas with the Phillies Brian Done with the Angels Jack with the Pirates Ryan Herald with the Cups Stephen K you have the Diamondbacks Douglas with the Orioles Matthew with the Red Sox Wade with the Cardinals Jack with the Indians Wade with the Nationals Adam with the Tigers Matthew with the Rays and Wade with the New York Mets So yeah, I'm just going to close the trade window People are really not going to trade for this right? I mean, I don't know it's a baseball Maybe a little different maybe I'll keep it open for like 30 seconds Maybe I'll also trade if not. All right, and then over here customer names again We'll see who wins those two spots at Diamond Icons And here's the baseball Good luck This is a baseball player guys, so that's the good thing Who am I I am a retired Pitcher in the MLB. I'm currently 53 years old born May 15 1967 batted right through right Uh debuted in 1988 My win-loss record in the MLB is 213 wins 155 losses. My ERA is 3.33 Strikeouts over 3,000 over 150 saves Play for three teams My whole career one team the longest And with the Red Sox and Cardinals for one season each And yes, Ryan got it right away Ryan got it right away And yeah That was quick Eight-time All-Star World Series champ 1985 with the Braves NLCI Young Award winner NLCS MVP silver slugger award Two-time NLCI wins leader two-time NLCI strikeouts leader and I'll save leader Retired number 29 for the Braves Braves Hall of Fame and part of the Baseball Hall of Fame in 2015 So there you go John Smoltz So that'll be going to the Braves, of course you played for them the longest There's the Beckett COA I go right on the sweet spot I don't know if I had a backwards amount, but I think it's this way. There you go. Very nice So who has the Atlanta Braves?  There's a little John Spaltz wiki Now let's give away those spots that have an icon. Remember top two names get in after Four and a two six times top two get in One two three four five and six six times Jason K and Wade Congratulations after six times you guys are both in on the break and coming up next is the break itself Appreciate it guys, jaskieskatesbreaks.com


Let's talk about the Hulu Exclusive, The Princess! Why did I watch this movie? From the director of Nothing and the writers of Less.  And when I say basic, I'm not underselling that word. It's about a princess who's locked in a tower and forced to get married and she fights her way out of it. Damn it. That's it. That's the whole, that's the whole kitten caboodle. And the main draw of this movie as I've already stated is Joey King, who, in fact, isn't related to Martin Luther King. I looked that up. Contrary to popular belief, no affiliation at all. The film opens with a beautiful CG rendering of a castle. Specifically, the tower, our young Joey King princess, is locked inside. We're greeted to a handcuffed heroine on a bed trying to break free. Now, Joey King has reinvented herself. It looks like as an action star doing this and bullet train, which is coming out soon.   Probably would have died at the first. But we're living in a fairy tale movie world, right? Where anything goes and everything actually goes. There is tons of action in this movie. Honestly, I think this movie has more action than any other film I've ever seen.  It's non-stop. It's like action set piece for five minutes, talking for one minute, action set piece, talking. Unfortunately, that's it. It becomes very, very stale. And I won't even knock the action that much. Some of it's pretty creative. It looks kind of cool in a fun Disney afternoon way. This thing is rated R. I have no idea why. I just, I just cannot fathom what they were thinking making this an R rated movie. There's nothing sexy about it. There's no nudity. There's no swearing. It is entirely for the action. Like stabby stabs and blood. There isn't anything really even that gross or graphic as far as the action. So why not just pare it down to a PG-13 or even a PG because the movie seriously looks like it's a Disney plus MCU show. And that's not a compliment. A lot of the action is choreographed, which is equally as impressive. Especially when you take into account they're doing a Jason Bourne shaky cam approach most of the time. On some occasions the director does let the shot breathe for a bit and we do get an extended back and forth sword play sequence. But most of the time this camera's moving around. It's dropping with people. It's popping back up. It ebbs and flows throughout this thing. And look, Joey King's a cute actress. I'm not gonna deny that. But the director needs to calm the hell down with these camera shots. He's up in her grill all the time. And like me, she kind of has a larger nose. So it's not the most attractive thing to look at. It's just like, it's just real up there. Back the camera up a little bit. Take a more flattering angle for this poor girl. Because it's an R rated movie, you're gonna alienate a lot of the audience. I assume they're going after the kissing booth teen crowd. I would imagine 15 to 20 year old girls watching a love triangle show. To watching a medieval film where a girl escapes a prison by killing everybody she sees. I'm not sure it's a one to one with that audience. When I think badass female action movies, I go kill Bill. I turn to Underworld. I look at even Kate that came out a year or two back on Netflix or Atomic Blonde. Like they make lots of cool badass female movies. This is not one of them. This is just silly nonsense. The cinematography makes it seem like it's more childish than it's supposed to be. Colorful. The characters are really clean. Even our main hero ends up walking away with just a slice on the arm and a little nick on the lip. Which she has the entire film.   I'm like, what? What happened? This movie reminded me of something I would make with my buddies when I was younger. Where we don't really have a plot outside of just like a really loose idea of what we want to do. But really it's an excuse to do a bunch of different over-the-top fight sequences. And again, this movie has a ton of them. They are varied. They're using different weapons. There's an evil chick that's like a female scorpion who has a whip with a blade on the end. Get over here! Except there's no cool one-liners in this either. Man, I miss one-liners. I miss snappy dialogue. I don't remember anything in recent months or years even where I can say that's a quotable line. I'm gonna start saying that. Anyway, the budget's clearly not there for what they want to do either case. There are some attempts to try to make things a little bit more grand. A little bit more grandiose than they can be. But a lot of times they do what they used to do in the late 90s, early 2000s, which is Mesh, a CG character with a live-action one.   They do that like three times in this one. Once when she falls off, like through a railing, another time she gets pushed out a window into the water. It looks so bad and I love it. That's the shlock I'm here for. I wish there was more of that in this film than I might have been more interested in getting through it.  That's the level of quality we're looking at there.  We got to get this out. Hulu needs this movie right away so he can get three more subscribers onto the platform. So there are my thoughts on The Princess. Should you watch it? Absolutely not. Why did I?  Maybe just find a couple of the clips on YouTube of the action. That's really all you need. It really is just kind of a series of different set pieces featuring Joey King yelling a lot, going feral, fighting some guys with swords, doing a lot of spins, and not looking great either.  It's Joey King kind of frumpy, hair is wild, that nose is right up in your face. It's just nothing really pleasing about this. You know, when I watch action movies, whether it's male or female, I want the dude or Gal to look badass while they do it. This is missing key ingredients. No badass one-liners, not looking cool while you're doing it, and a villain so lame, you gotta wonder why they even bothered. Alright, those are my thoughts on The Princess. Did you check it out? I'm imagining not, but at least thanks for watching this regardless. Also, maybe think about subscribing if you haven't. As I post tons of movie and TV show related content here all the time, would love to have you stick around. If you are a subscriber already, make sure to hit that notification bell so they show up in your feed. There's a lot of subs on this channel. I'm not seeing that correlation with the views. I gotta, I gotta get it back. Gotta get it up there. And hopefully, yeah, hopefully I'll see you in the next video. Maybe the views are low because I'm reviewing movies like The Princess. That's a possibility. That's something I should probably think about. Since you're still here, maybe think about joining me on Patreon at patreon.com slash Adam Does Movies or become a member right here on YouTube via that YouTube Join button. It gives you access to exclusive videos. You get little badges. A couple other perks, but really it's for you to say, hey Adam, I like what you're doing. Here's a dollar. Here's 10 bucks a month, whatever you can give. And I'd appreciate it. Thanks.


Welcome to lecture 38 on measure and integration. Today, we will start looking at the notion of absolute continuity of measures. We have started this concept in the previous lecture, but we will do it in detail in today's lecture. So, we will start with looking at what is called one measure being absolutely continuous with respect to another measure. And then we will prove an important theorem called Radon-Rickardim theorem for absolutely continuous measures. So, let us start recalling what is absolutely continuous measure. So, if two measures mu and nu given on a measurable space XS, we say nu is absolutely continuous with respect to the measure mu. If for any set E in the sigma algebra S, mu of E equal to 0 implies nu of E equal to 0. That means, if a set E has got mu measure 0, then it should imply that mu measure of the set E is also equal to 0. So, in that case, we write this relation by the symbol that nu with this special symbol, which is less than twice printed. So, it is called absolutely continuous with respect to nu and this is denoted by this symbol. And we looked at an example of absolutely continuous measures. So, we said let us take a function f, which is non-negative measurable on a measure space XS mu and let us integrate this function over a set E in the sigma algebra. So, this integral f is fixed, mu is fixed, E is varying and this is a non-negative number, which we denoted by nu of E. And we had shown when we defined the integral for non-negative functions that nu of E is a measure and it has a special property that if mu of E is equal to 0, then nu of E is also equal to 0. So, this measure nu of E, which is defined via the integral of a non-negative function f over a set E implies that this measure nu is absolutely continuous with respect to mu. Let us give a characterization of absolutely continuous measures in terms of what is called epsilon delta definitions, which looks similar to absolute continuity of functions. So, we want to prove the following, namely if mu and nu are two measures such that nu is absolutely continuous with respect to mu, then the following holds that if nu is finite, then for every epsilon bigger than 0, one can find a delta bigger than 0 such that whenever nu of E is less than epsilon, nu of E is less than epsilon whenever mu of E is less than delta. That means, given an epsilon you can find a delta, so that whenever for a set the measure mu of E is less than delta that should imply nu of E is less than epsilon. So, let us prove this result. So, we are given that nu and nu are measures on the measure measurable space X s and nu is absolutely continuous with respect to mu and nu is finite. To show for every epsilon bigger than 0, there is a delta bigger than 0 such that mu of E less than delta should imply nu of E is less than epsilon. So, the proof of this is by contradiction. So, suppose this claim is not true, that will mean what? So, claim is for every epsilon there is a delta, so that means that there is an epsilon such that then for every epsilon bigger than, no that means then there exists epsilon bigger than 0 such that for every delta there exists a set E belonging to the sigma algebra with a property whenever mu of E is less than delta, but mu of E is bigger than or equal to epsilon. So, if we assume that the required claim is not true that will imply that there is a number epsilon bigger than 0, so that for every delta you can choose a set E, of course this E will depend on delta such that mu of E is less than delta, but mu of E is bigger than or equal to epsilon. So, let us apply this result for, so apply this for delta equal to 1 over 2 to the power n. So, that will give us the following, so when I do that, so for every n for every n there exists a set E n belonging to S such that mu of E is E n is less than 1 over 2 to the power n, but mu of E n is bigger than or equal to epsilon. So, this is what we get if we assume our result is not true. Now, let us define a set E n to be equal to union of E n E k from k equal to 1 to k equal to n to infinity and a to be equal to intersection of A n's n equal to 1 to infinity. Let us note the following. The set A n, so mu of A n is less than or equal to sigma mu of E k k equal to n to infinity and mu of E k is less than 1 over 2 to the power k and summation n equal to 1 over 2 to the power n. So, this is going to be equal to 1 over 2 to the power n plus 1. So, mu of A n because mu of E k will be less than 1 over 2 to the power k. So, this says mu of A n is less than or equal to 1 over 2 to the power n and this A n is union of n to infinity. So, as n increases, these A n's are going to be smaller and smaller. So, A n is a decreasing sequence and it decreases to the intersection namely A. So, thus mu being finite, A n decreasing to A will imply, so this will imply mu being finite. So, this will imply that mu of A is equal to limit n going to infinity mu of the set A n. But mu of A n, A n is the intersection of A n. So, A n is union of E k and so let us observe that is bigger than or equal to mu and mu of A n is summation. So, it is bigger than or equal to mu of E n because A n is union of E n's because A n is union of E n's. So, A n includes E n. So, mu of A n is going to be bigger than or equal to mu of E n which is bigger than or equal to epsilon. So, that implies, so this along with this implies that mu of A is bigger than or equal to epsilon. But we just now observed that mu of A n was less than or equal to 1 over 2 to the power n plus 1. So, what does that imply? So, that implies that mu of the set A and because A is equal to intersection of this, so mu of A is less than or equal to mu of A n for every n. So, less than or equal to 1 over 2 to the power n plus 1 for every n. So, that implies that mu of A is equal to 0. So, what we are done is assuming that the required condition does not hold, we have shown that there is a set A, so that mu of A is 0, but mu of A is not equal to 0, it is bigger than or equal to epsilon. So, which is a, so this is the contradiction. So, that implies that what we assumed is not true and hence we have the required claim namely that if mu is absolutely continuous with respect to a measure mu and mu is finite, then for every epsilon bigger than 0, there is a delta bigger than 0 such that mu of A less than delta implies mu of the set A has to be less than or equal to epsilon. So, this is what we have proved. So, we have shown that if mu is finite, then the condition that mu is absolutely continuous with respect to mu implies this required claim. Now, let us prove actually the converse of this statement is also true namely for every epsilon bigger than 0, if there exists a delta such that mu of E is less than epsilon whenever mu of E is less than delta, then mu is absolutely continuous with respect to mu. So, let us prove the converse. So, converse says the following that we have the property that for every epsilon bigger than 0, there is a delta bigger than 0 such that mu of asset E less than delta implies mu of E is less than epsilon and we want to claim that this property means that mu absolutely continuous with respect to mu. Let us suppose, so let mu of E be equal to 0. So, if mu of E is equal to 0, then for every epsilon, for every epsilon whatever delta we take for every delta mu of E is equal to 0 is less than delta. So, that will imply by the given property that mu of E is less than epsilon. So, mu of E is less than epsilon for every epsilon. So, that implies mu of E is equal to 0. So, saying that for every epsilon there is a delta such that mu of E is less than delta implies the mu of E is less than epsilon implies that mu of the measure mu is absolutely continuous with respect to mu. So, the converse is easier and it is true even if mu is not finite. So, we do not use anywhere the fact that mu is finite. So, anyway we require mu to be finite. That means absolute continuity and mu finite implies this condition that for every epsilon there is a delta such that mu of E less than delta implies mu of E less than epsilon. For the converse we do not need this property. So, this is one characterization of absolutely continuous measures. Let us recall that we have defined we have characterized all measures on the real line on the Borel sigma algebra. We had shown that if a measure mu is absolute is given a measure mu on the collection of all Borel measurable sets in the real line there exists a monotonically increasing right continuous function such that for any interval a comma b mu of a b is given by f of b minus f of a. So, that is the that gave us the characterization of all tautably additive set functions on the sigma algebra Borel subsets of real line. Using that we would like to characterize what are all absolutely continuous measures on the real line with respect to the Lebesgue measure. So, the theorem states the following namely let f be a monotonically increasing right continuous function and mu f be the measure induced by this monotonically increasing right continuous function f on B R. Then the claim is that this measure mu f is absolutely continuous with respect to the Lebesgue measure lambda if and only if the function f is absolutely continuous on every bounded interval. So, we would like to prove this result. So, this will give us that what are all measures which are absolutely continuous with respect to the Lebesgue measure it ties up with the property of the function f being absolutely continuous. So, this relates the two concepts absolutely continuous measures and absolutely continuous functions on the real line. So, let us look at a proof of this. So, let us assume that f is monotonically increasing and right continuous and mu f is the measure on the Borel sets which is given by for the left open right close interval A comma B it is defined as if you recall we defined it as f B minus f of A and then we showed that this mu f is the measure is a measure which we called as the measure induced by the function f. So, this is given. So, let mu f be absolutely continuous with respect to the Lebesgue measure to show that the function f is absolutely continuous on every interval say A to B to show that f is absolutely continuous on every interval A to B what we have to do we have to show that for every epsilon bigger than 0 there is a delta. So, to show for every epsilon bigger than 0 there is a delta bigger than 0 such that if you take a sequence of intervals say A i B i are finite disjoint intervals these are finite disjoint intervals in the interval A B with the property with the property that sigma of B i minus A i is less than delta then that should imply that sigma i equal to 1 to n f of B i minus f of A i is less than epsilon. So, this is what we have to show. So, let us fix. So, let epsilon greater than 0 be given. So, let us start with an epsilon bigger than 0 be given. Now, since mu f is absolutely continuous with respect to lambda there exists delta bigger than 0 such that lambda of set E less than delta will imply that mu f of E is less than epsilon. So, this is by the property we just now proved that absolute continuity is equivalent to this property and mu of f on the interval A B is finite such that for every E inside belonging to the Borel sigma algebra of the interval A B this is true. So, in particular if E is a finite disjoint union of intervals A i B i, if A is a finite disjoint union of intervals A i B i inside such that lambda of E such that lambda of E such that lambda of E which is equal to sigma B i minus A i is less than delta. So, that will imply that mu of f of this set E, but mu of f of this set E is nothing but f of B i minus f of A i summation i equal to 1 to n is less than epsilon. That is because we are just now given epsilon we have chosen delta with that property. So, in particular we are applying this for a set E which is a finite disjoint union of intervals A i B i inside the interval A B.  So, that implies so hence this proves that f on A B to R is absolutely continuous. So, one way we approved that if so we approved that if f of mu of f the measure induced is absolutely continuous with respect to the Lebesgue measure then the corresponding function f the monotonically increasing right continuous function f which is inducing that measure is also absolutely continuous. Let us look at the converse of this statement that we are given that the function f capital F which is monotonically increasing and right continuous is also absolutely continuous. Then we want to show that the corresponding measure mu f is absolutely continuous with respect to the Lebesgue measure. So, let us prove that fact. So, let us prove that. So, assume that mu f is absolutely continuous with respect to lambda to show. So, we just now showed no we have to show the other way round. So, this is not this is just now we have shown. So, assume that f is absolutely continuous to show. So, we have to show that mu f is absolutely continuous with respect to lambda. So, this is what we have to show for the other way round proof. Let us assume. So, let E belong to the R and lambda of E equal to 0. So, to show mu f of E is equal to 0. So, this is what we have to show mathematically. Now, let us observe first of all. So, showing that mu f of E is equal to 0. So, enough to show that mu f of E intersection every interval A to B is equal to 0 for every interval A, B. So, then by we can split E into every interval. So, we can countable additivity will give us that this is 0 for every E. So, let us assume that we have got. So, enough to show that this is equal to 0. Now, since lambda of E is 0. So, lambda intersection A, B is also equal to 0. That means, this set E intersection A, B is a set of Lebesgue measure 0. So, by the properties of sets on Lebesgue measure 0, we can find. So, let us for a given epsilon, for a given epsilon, we can find intervals say A n, B n. We can choose them to be left open, right closed, n bigger than or equal to 1, 2 and so on, such that this set E, which is a null set intersection A, B is covered by these intervals A n, B n and the total length of this and sigma B n minus A n, n equal to 1 to infinity is less than epsilon. So, total length of this is small. This is by the property that the set by the property that E is a null set. So, E intersection A, B is a null set. So, by the definition of after measure, if you like, you can find a sequence of left open, right closed intervals, which cover this set and the total length of these recovering intervals is small, is less than epsilon. So, now let what we want to show? Our aim is to show that the function f is absolutely continuous. So, let us take any number say alpha, let alpha bigger than 0 be given, then we have to, it is enough to show that mu of that thing is equal to. So, what is to be shown? We are given that f is absolutely continuous, then by absolute continuity, by absolute continuity of f, there exist by the absolute continuity of f, there exist some delta bigger than 0 such that whenever say that whenever intervals say intervals A n, B n are disjoint in A B with sigma B n minus A n sum n equal to sum 1 to k, finite number of disjoint intervals A B less than delta will imply that f of B n minus f of A n n equal to 1 to k is less than alpha. This is by the absolute continuity of the function f, which is given to us. Now, we start with given any alpha bigger than 0, we find a delta with this property and now for this delta, we apply our earlier thing that lambda of this was a null set. So, for any given epsilon, we will use this when epsilon is equal to delta, because when epsilon is equal to delta, we will have the summation of these intervals less than delta and that will imply, so that will imply the corresponding, so by, so let us call this thing as star, so this thing as star, so by star with epsilon is equal to delta, so by star with epsilon equal to delta we have, so for, so we will have that sigma of f B n minus f of A n n equal to 1 to k is less than alpha for every k. So, this happens for every k, so that implies that sigma of n equal to 1 to infinity f of B n minus f of A n is also less than alpha, because this is happening for every k, but that implies that mu of A intersection AB, which was mu f of this, which was less than or equal to, because A intersection AB was contained in the union of intervals A n B n, so it is less than or equal to sigma mu f of A n B n, n equal to 1 to infinity and this is equal to sigma n equal to 1 to infinity of f of B n minus f of A n, which is less than alpha. So, what we have shown is that for every alpha mu f of E intersection AB is less than or equal to alpha, so that implies, so this happens, because this is happening for every alpha, so this implies that mu f of E intersection AB is equal to 0, because this is happening for every alpha, so we can let alpha go to 0. So, hence we have shown that lambda of E equal to 0 implies this mu f of A intersection AB is equal to 0 for every AB and so that implies, because this is happening for every AB, so this implies that mu f is of E is equal to 0, so hence mu f is absolutely continuous with respect to lambda. So, this proves the other way round theorem, so this completes the proof of the theorem that mu f is absolutely continuous with respect to lambda, if and only if the function f is absolutely continuous on every bounded interval. So, this completely characterizes and ties up the notion of absolutely continuous measures on the real line with respect to Lebesgue measure with absolutely continuous functions on the real line. Next, we want to prove a theorem called, a theorem called von Neumann theorem, which is a very nice theorem and gives a, it uses very nicely and very intelligently the fact that the dual of the L2 of a measure space is itself. That we called as the Ries representation theorem, namely that if T is a continuous linear functional on L2 of a measure space, then it is essentially given by the inner product, by the inner product. So, this is used very effectively, will not be giving a proof of this theorem, those who are interested can read the text book, but we will see how this theorem is used to prove some results about measures. So, let us first state this theorem called von Neumann theorem. So, the theorem says, let us take two measures mu and nu, which are sigma finite measures on measurable space x s. Then, it says, there exists mutually disjoint sets x i, a measurable sets such that the following properties hold. First of all, this x 1, x 2, x 3 give a partition of the space x. So, x is partitioned into three parts, x 1, union x 2, union x 3. One x 3 and x 1, so nu of x 3 is equal to 0, that means nu has no, for any subset in x 3, the measure of a set is equal to 0. So, that means nu at the most gives values to subsets on x 1 and x 2. On the other hand, mu of x 1 is equal to 0, that means mu gives values to subsets possibly in x 2 and x 3. So, nu of x 1 and nu of x 3 is equal to 0, mu of x 1 is equal to 0. On the set x 2, there is a function g, which is a non-negative measurable function such that for every subset E of measurable subset E of x 2, nu of E can be written as integral of the function g over the set E. So, it in some sense describes, so it says, let us take, this is my set x and we have got two measures mu and nu. It says we can decompose into three parts x 1, x 2 and x 3 into three parts x 1, x 2 and x 3 into three parts x 1, x 2 and x 3. On this part, nu of x 1 is 0, on this part mu of x 3 is equal to 0. So, in this part nu is 0, in this part mu is 0. On this part x 2, this nu of any set E, for any set E here, it can be written as integral over E of g d mu. So, this property holds on this set. So, this is a decomposition of the phononium 1. So, let us just recall. So, the phononium 1 decomposition theorem says that given two measures nu and mu and nu, which are sigma finite of course, we can decompose x into three parts x is equal to x 1, union x 2, union x 3, nu of x 3 is equal to 0, mu of x 1 is equal to 0 and on the middle part x 2, the measure nu can be represented in terms of the measure mu by the property that nu of E is equal to integral g d mu. So, this is called phononium 1's theorem and it is very useful theorem. We will see soon. So, using this theorem, we prove what is called the Lebesgue decomposition theorem. So, Lebesgue decomposition theorem says the following that suppose mu and nu are two sigma finite measures on a measurable space x s, then it implies that there exists sigma finite measures nu A and nu S with the following properties. Namely, this measure nu can be written as a sum of two measures nu lower A and plus nu lower S. So, the measure nu can be written as the sum of two measures nu of A plus nu of S and what are the properties of these two measures? The first property says that measure nu of A is representable in terms of the measure mu via integrals. So, it says nu of A for any subset E is integral of a non-negative measurable function f over the set E. So, it says there exists a unique non-negative measurable function f such that to compute nu of A of any set E, we just integrate f over the set E. The second part says it describes what is the measure nu S. It says there is a set A such that mu of A complement is 0 and nu S of A is equal to 0. That means mu and nu S are setting on disjoint sets. Mu of A complement is 0. So, that means mu sits on A and nu S of A is equal to 0. So, nu S is on A complement essentially. So, this is what is called Lebesgue decomposition theorem. So, we want to show that how it arises out of as an application of von Neumann's theorem. So, this is also part of the consequence that such a decomposition is unique. .. So, let us look at by von Neumann's theorem. Given the measures nu and mu, we have disjoint sets x 1, x 2 and x 3 such that the following operative holds. We recall that x is equal to x 1, union x 2, union x 3 and nu of x 3 is equal to 0 and mu of x 1 is equal to 0. So, mu does not give any mass, it does not give any measure to this set x 1 and nu does not give any measure to this set x 3. On x 2, we recall that for every set E measurable set, if we look at E intersection x 2, then we can compute this measure as an integral of a non-negative measurable function g over the set E intersection x 2. Moreover, recall this is a non-negative, g is a non-negative measurable function and g is equal to 0 on the complement of the set E 2. So, that is the because the measure nu on x 3 is equal to 0. So, this is the by von Neumann's theorem. Now, it is easy to define what should be our measures nu A and so on the set x 2, we should define nu A to be equal to nu on x 2. So, let us define, let us put A equal to x 2 union x 3 and on this set for every set E belonging to S nu of A of E is defined as nu of A intersection E and on the complement of this part. So, nu S of E that is going to be E intersection x 1 because x 1 is the complement of A that is A complement. So, define nu A nu the measure nu as nu of A intersection E restrict nu to E and restrict nu to x 1 to get the measure nu S and now obviously these two are nu S and nu A are measures that is obvious from the definition and also is clear from the definition that the measure nu is nothing but nu A because nu A is on A and nu S is on A complement.  So, this satisfies the required properties only we have to check that nu of A is given by the integral and that is obvious because nu A of E is nu of E intersection x 2 union x 3 by the definition because A is x 2 union x 3 and on x 2 it is given by E intersection x 2 integral g d mu because nu of x 3 is equal to 0. So, nu of A is given by the integral. So, that proves the theorem except for the fact that at present g is defined only on x 2. So, there is not a issue we can extend it to the whole by putting it equal to 0 then it has the required property that f is defined is non-negative measurable function defined on the whole space x and nu A of E is given by the integral. So, that proves the Lebesgue decomposition theorem and the uniqueness is only a manipulation of the measures. So, which will really leave it as a reading exercise for the reader to verify. So, uniqueness we will assume the uniqueness part of it. So, Lebesgue decomposition. So, let me go back and state understand what is Lebesgue decomposition theorem. It says that given two sigma finite measures on a measure space the measure one of the measures say let us nu can be written as a sum of two measures nu A and nu S where nu A is given by integration and nu S sits on a part which is complement to the part of mu of A. So, this is nu of A is given as a integral and mu of A complement is same as nu S of A is equal to 0. So, this theorem is called Lebesgue decomposition theorem. So, this measure nu S that we have defined just now gives a let us make it as a definition. So, two measures mu and nu are said to be singular with respect to each other or we say mu is singular with respect to nu if there is a set say that mu of the set E is 0 and nu of the E complement is equal to 0. That essentially says we can decompose the space x into two parts E and E complement and mu sits on one part and nu sits on the other part. So, such measures are called singular and it is obvious that if mu is singular with respect to nu then nu is singular with respect to mu. So, it is a commutative relation of singularity while absolute continuity was not. So, nu absolutely continuous with respect to mu need not imply mu is absolutely continuous while the singularity is true that namely if mu is and this singular is also written as mu perpendicular. So, this is also read as singularity is also said to mu is orthogonal or mu is perpendicular to nu and written as mu perpendicular to nu. So, Lebesgue decomposition theorem and now can be stated in terms of this singularity that given two measures which are sigma finite on a measure space x s there exists sigma finite measures nu a and nu s such that the following properties hold namely nu is decomposed into two parts nu a plus nu s where nu of a is absolutely continuous with respect to mu and nu s is orthogonal with respect to mu. So, this is the decomposition that essentially it says that the measure nu has got absolutely continuous part and absolute continuous part says you can obtain nu of a via integration and singular part says that this is the other part which is completely orthogonal to mu. So, they says disjoint says you cannot do anything there they are disjoint sets they set on what one says they are their sports are disjoint essentially. So, this is what is called Lebesgue decomposition theorem and as a consequence of this we will get what is called the radon recursive theorem which characterizes absolutely continuous measures and it says that if two measures mu and nu which are sigma finite on a measurable space x s be such that nu is absolutely continuous with respect to mu then there is a non-negative measurable function f such that nu of e is given via integration of f over the set e. So, that completely characterizes absolutely continuous measures recall if we define nu of e by this then we have already shown that was the beginning of our analysis saying that any measure nu defined in terms of integral with respect to mu is absolutely continuous and this is the converse part of it namely if nu is absolutely continuous with respect to mu then there must be a non-negative measurable function f such that nu of e is equal to integral of f over e with respect to the measure mu. And proof is obvious from the Lebesgue decomposition theorem and the uniqueness part of it because we know that nu is absolutely continuous with respect to mu. So, when we apply Lebesgue decomposition theorem to the measures nu and mu nu will be decomposed into two parts the absolute continuous part and the singular part but there is no singular part. So, there is only absolutely continuous part and absolutely continuous part we have already seen in Lebesgue decomposition theorem is given by integrals. So, this is a direct application of Lebesgue decomposition theorem and this function f is also unique in the sense that if there are two functions then f must be equal to g almost everywhere and that happens because if there is another function g with the same property then integral of f over every set e is equal to integral of g over every set e and that implies that f must be equal to g almost everywhere that we have seen earlier. So, Radon-Degardim theorem the proof is an application of Lebesgue decomposition theorem and Lebesgue decomposition theorem is an application of von Neumann's theorem. So, once again saying that nu is absolutely continuous with respect to mu by Lebesgue decomposition theorem nu of a must be equal to nu because that is absolutely continuous and nu of s is equal to 0. So, that says that nu of e is given by integral over f by the Lebesgue decomposition theorem and as I said we said uniqueness is obvious because integral f is equal to integral g must imply that f is equal to g almost everywhere. So, this is so Radon-Degardim theorem is one of the most important and subtle theorems of our subject because just from the existence of same null sets mu of e equal to 0 implies nu of e equal to 0. This property simple property about null set says that nu must be obtainable from mu via integration. It is really a deep and amazing theorem of our subject and let me also point out there are many proofs available of this theorem. We have given a proof which is via von Neumann's theorem and von Neumann's theorem uses the fact that the dual of L 2 is L 2. There is another purely measure theoretic proof of this, but that goes into the realm of what is called signed measures. So, one looks at signed measures and then one decomposes a signed measure. There is something called a Han decomposition theorem that every signed measure is a difference of two measures and then from there one disuses Lebesgue decomposition theorem and then comes to Radon-Degardim theorem. That is another route possible for proving this theorem. Both the proofs are available in the text and we have outlined here only one proof which is more function theoretic using that dual of L 2 is L 2. This gives the notion of absolute continuity also gives rise to the notion of what is called the derivative. Let us define that. Whenever two measures mu and nu are sigma finite and nu is absolutely continuous with respect to mu, Radon Degardim theorem says that nu of E must be given by a function, a unique function f. This unique function f is called the Radon Degardim derivative of the measure nu with respect to mu and is denoted by d nu by d mu. So, here are some simple properties of this Radon Degardim derivative which are very much similar to the derivative of functions namely if mu 1, mu 2 and nu are sigma finite measures and if mu i each mu 1 and mu 2 is absolutely continuous with respect to mu then mu 1 plus mu 2 is also absolutely continuous and the Radon Degardim derivative of the sum is equal to sum of the Radon Degardim derivatives of course almost everywhere. So, very much similar to the derivative of the sum is equal to sum of the derivatives for functions and similarly if mu 1 is absolutely continuous with respect to mu 2, this is a mistake here and mu 2 is absolutely continuous with respect to mu 1 that means both are absolutely continuous with respect to each other then the product of the derivative is equal to 1. So, that is the second property. So, here it should be mu 2 absolutely continuous with respect to mu and finally if nu is absolutely continuous with respect to mu 1 and mu 1 is absolutely continuous with respect to mu 2 then there is a kind of associative property namely this implies that nu must be absolutely continuous with respect to mu 2 and the derivative.  So, it is like a chain rule for the derivative functions. So, with that idea of this set of ideas namely absolutely continuous functions and absolutely continuous measures is complete and in the remaining next lecture we will look at some special properties of sequences of measurable functions and the various ways they can converge to a function f. Thank you.