I'm here with Joan Carling who's the Secretary-General for the Asia Indigenous People's Pact. How are you today Joan? I'm fine, quite an overwhelming day of listening to all the presentations. Yeah I think it's been a good conference so far. I'd be interested to know from you to start off with some of the discussion that's emerged in the ADP is around monitoring and the contribution that can be made to the measuring, reporting and verification process when it comes to carbon emissions reductions which is a very important component of Red Plus. So through your work what have been your experiences so far with the way in which Indigenous Peoples are engaged with MRV and measuring, reporting and verifying carbon. Okay let me first start to say that Indigenous Peoples in Asia comprise 70% of the total Indigenous Peoples in the world and we're talking of more than 200 million of Indigenous Peoples and majority are located in the forested areas as part of their territory so that means Red Plus and forest conservation in general is very, very critical to Indigenous Peoples and that's also the reason why a lot of Indigenous Peoples have decided to engage in the process and also to send the message that for us forest is not just carbon, it has other co-benefits and it has multiple values that has to be taken into account and thereby it requires the full and effective participation of Indigenous Peoples in all processes of Red including MRV as well as to ensure that our collective rights particularly to our forest customary rights are recognized and respected and that we are entitled to equitable benefit sharing throughout the phases of Red. Now if we go to the MRV I think there are two components that requires the full engagement of Indigenous Peoples one is the issue of the monitoring of carbon and the second is also the monitoring of the non-carbon benefits as well as the enhancement of biodiversity and the way in our rights are being respected so it's also a matter of monitoring the safeguards and the benefits, the entitlement to benefits to Indigenous Peoples I think that is very, very critical if we want the MRV also to be able to provide for the needs and priorities of Indigenous Peoples. In the UNFCCC discussions that are currently occurring this year there's an emerging issue around the safeguards information system and that looks at the adequacy of the guidance that exists at the moment for the safeguards information system and the type of information that will be fed into the safeguards information system and some recent research that's been undertaken by C4 has identified land tenure as being really the number one issue or the number one challenge when it comes to being able to properly and adequately implement Red Plus and I think back to, I think it probably would have been 2009, 2010 when there was a very strong no rights, no red campaign that was moving forward and I'd be interested to know what your thoughts might be when we think about the types of information that would be useful for a safeguards information system and what your thoughts might be there in the context of land tenure Do you think that would be a useful type of information to be fed into a safeguards information system and reported on at an international level? Certainly because that's the crux of the matter as far as Indigenous Peoples are concerned and that requires developing some key indicators in terms of how land tenure is being addressed For example, one key indicator is how much land are demarcated for the recognition of land tenure of Indigenous Peoples and how our ways of managing our resources are also being acknowledged and recognized for defining the terms of benefits for the entitlement to benefits not only in terms of carbon but also the non-carbon benefits The other area that has to be accounted for is the issue of collective rights of lands and not just the individual rights because that's now, I fear, as the trend in terms of recognizing community land rights that they're breaking up community land rights into individual titles which completely undermines the whole issue of collective ownership and management of forest and other resources by the people that benefits everyone in the community and that opens up the possibility to lead capture of the benefits So for example, if we look at past experience like the PES, the Payment of Ecosystem Services for community forest management in the past, if we look at Vietnam who's been rich in terms of this issue the way it has been arranged is through individual lease of former community lands So suddenly the other members of the communities became the workers of their own community land and being paid by the person who leased So suddenly the relationship, I mean the elite capture was there but also the system is not anymore equitable because when we talk of equitable it should also account for providing the needs of the poorest of the poor as well as accounting for the needs of women So we're not just talking equitable in the abstract sense when you talk of how land tenure is going to be managed and how entitlements are going to be given to the communities And I think the issue of tenure also goes beyond one of just simply land tenure as well because when you start to move into the discussion about benefits whether they're financial or non-financial types of benefits that may derive from these types of frameworks then you also get into discussions around rights to carbon that may exist and another area that I find interesting is the issue of intellectual property and Indigenous peoples and intellectual property I know that there's been, especially in a pharmaceutical context there's been a big issue and it's not really something that has come up to any significant extent in the context of the climate change negotiations I think it was raised by the Philippines at the ADP inter-sensional recently in the context of technology transfer as performing a part of the new climate agreement and so I'd be interested to know, we have these systems coming through where there's a lot of money being spent on MRV systems and technology and we have systems around safeguards monitoring I'd be interested to know from you some examples of unique approaches that would come from Indigenous peoples and what that may mean or how that may equate to the potential for intellectual property to exist I think the problem now of the issue of intellectual property rights is that it is privatized, it's in a private context where the owner is entitled to the benefits of that particular knowledge or skill but from the perspective of Indigenous peoples and from our traditional values, we look at these things for the common goods so you don't privatize something that can be shared for the common goods so when we're talking of resources, it's a resources that should be shared by everyone so that everybody benefits so I think that there's a contradiction in the way we look at things that it's a common property, we operate from the value of common property and for the common goods so for example you're talking of carbon rights we will claim carbon rights not in the context of private individual ownership but the ownership of the community and thereby the benefits should be also for the community in an equitable manner so that is where we are coming from so when you talk of carbon or even the use of medicines it's for the benefit of the people who are sick and needing that kind of medicine and it's not for somebody to take ownership of that plant and sell it for somebody who is sick so that is the area that we are trying to express or mainstream our views that we should always look at this in the context of the common good and not for private or individual profit or benefit I'm from Australia and so in Australia there's been a lot of interesting developments around Indigenous peoples' land rights related issues and native title in Australia and it has largely maintained a circumstance where it is that collective ownership and I think that it is it certainly does raise serious concerns where that begins to be broken down so that's been very useful we're in Indonesia at the moment it would be useful, I know that AIPP has done some work and looked at some of the issues here in Indonesia I think that it's perhaps worthwhile mentioning what I think was a landmark decision of the constitutional court here in Indonesia do you see there is some progress being made in Indonesia around the tenure issue arising from that decision have you noticed that there's been a move in the right direction or are you seeing things going possibly in a different direction here I think the constitutional court decision is really a milestone achievement but it also requires a complete turnaround of the mindset particularly of the forest department in Indonesia as well as some local governments because from what I gather from my colleagues here from Aman is that the way the decision is going to be implemented is according to local governments because of the autonomy law of which they will operate at the local level and they have different interpretations and different attitudes in terms of customary forest so it's still in the dark on how it's going to be implemented but the legal recognition already set the right direction and I hope that eventually indigenous peoples will benefit tremendously from this law and I think that the critical point now is for indigenous communities in Indonesia to really claim it on the ground like what they've been doing they're already putting marks in their territories they're already doing demarcation of their territories Aman has demarcated more than 4 million hectares of customary forest land so that has to be recognized legally by local authorities and by the national government so there needs to be further harmonization I think in terms of how they will operationalize that court decision to ensure that indeed the Masyarakat adat of Indonesia are going to be protected by this law I'm hoping to see some progress made there too I think Aman have done some brilliant work from an legal perspective I think they've done some very brilliant work there so I think that going forward I think that it's in good hands as well I just want to add that perhaps in all my work with indigenous peoples in Asia I think red has opened up really a lot of discussions and has surfaced and highlighted indigenous peoples in a manner that has never happened in the past and it has put on the table the issue of land tenure, particularly collective land tenure of indigenous peoples so now governments like Vietnam, Thailand are moving into that direction which has never been considered in the past so there are very positive developments and positive signs along the recognition of land tenure of indigenous peoples however there's still a long way to go in terms of really the governments having the political will to really recognize and respect collective land rights and allowing people to decide how their resources are going to be used and I think genuine partnership along the recognition of the collective rights of indigenous peoples is the only way that red is going to succeed in a manner that co-benefits and equitable development is going to take place I agree and also I think also building on that point if you go back a few years there was a very I think clear sort of tension that existed more so between conservation work that's being undertaken and indigenous peoples rights related issues and I think that red plus and the discussion that's been happening around red plus has done a great deal to move more in the direction of bridging those gaps as well so I think it has given rise to some very useful discussions but still as you say a long way to go I think so that's been a very good conversation and it's been nice to talk to you


Hello and welcome to our program sponsored by the U.S. Department of State as a lead-up to the Global Entrepreneurship Summit in Kenya from July 25th and 26th. GES highlights the U.S. government's commitment to fostering entrepreneurship around the world. Today we'd like to focus on African entrepreneurs. I'm Dante Desparte, founder and CEO of Risk Cooperative, a strategy, risk and capital management firm. Before I introduce our distinguished guest, we'd like to remind you to use hashtag on-tripAfrica or hashtag GES 2015 Kenya to tweet about this live event and to send us pictures. Also, don't forget to type your questions in the chat space at the bottom of the video player. I'm excited to be joined live in our Washington studio by Rahama Wright, a first-generation Ghanaian-American entrepreneur, founder and CEO of Shailene International, a beauty care cooperative that promotes economic empowerment through shade butter production. She's here today to share her unique experience and to answer your questions. I'd also like to extend a special welcome to our viewing groups in Port Louis, Dar es Salaam, Rabat, IRC Abijan and Addis Ababa, including all of you who gathered at our American Corners to watch this program. Now while we wait for your questions to come in, let's hear briefly from Rahama and Uganda. Thank you, Adante, for the great introduction. It's always an honor to talk about entrepreneurship and to share my story and to share the work that Shailene is doing to economically empower women in West Africa, specifically Ghana. I want to extend thanks to the Department of State for the invitation and just really want to have a really great conversation this morning. I started Shailene after serving in the Peace Corps and during that time I was a community health volunteer and worked at a community health center. And on a regular basis, women would come into the health center and they would have issues in terms of being able to pay for medicine. So as I started learning about the challenges women in my community had generating income, I did some research and started learning about shade butter and its connection to the lives of women in the Sahel region of Africa. And so I launched Shailene to help women take shade seeds, turn it into shade butter, connect it to the U.S. marketplace in a way that allowed women to generate living wages, as well as give consumers of shade butter in the U.S. an option to have the highest quality product on market. And so I'm really excited to hear some of the questions that will be coming from the viewers. And I don't want to give up too much information now. I just want to get a chance to hear from these young entrepreneurs who really want to know how to create their own businesses and how to link products to market. Thank you, Rahama. So let's turn briefly also to hear from some remarks from the U.S. Embassy in Kampala, Uganda. Hello, my name is Al Murphy. Definitely it's a pleasure to be here today to talk about such an important topic. I also met Rahama maybe about four or five years ago in the beginning of the presidential initiative Young African Leaders. I'm very impressed and happy to share the program with her also. Here in Uganda, we're very excited, especially this program would be very good for a lead up to the GES. Also, we have members here from entrepreneurs who are young African leaders, former young African leaders, and also from generation change and many others are here today. We have over 20 some participants. We're excited and ready to go and eager to go. So looking forward to participating today. Thank you, Uganda. So, Rahama, you've built an important business that empowers entrepreneurs and especially women. Can you give the audience more insights into your business model? Sure. So how Shailene is set up is we work with cooperatives. And these are shaped by cooperatives made up of women who have been organized. And what we do is we partner with these cooperatives. We do everything from helping them get access to training. We give them access to production equipment that they need to produce shea butter. And this is what the shea seed looks like. And so essentially, we provide the environment to enable these women to create a high quality product. And then we import the shea into the U.S. in addition to soap. And we do the packaging and we make it look great and pretty. And then we bring that product to market. And right now we distribute our products through Whole Foods Market, which is the number one natural and organic retailer in the U.S. That's fantastic. So let's let's see, turn to our audience in Uganda. I know there's a number of, you know, eager participants in the room and we can get the first live question from Uganda. Okay. Hi, my name is Evelyn Namara and I'm one of the participants who will be going to Nairobi for the GS Summit. And my question is there's lots of female entrepreneurs who are rising up and setting up businesses. But one of the biggest challenges is access to finances. So do you have any maybe databases or resources that you can share for women entrepreneurs in terms of seed funding? Thank you. That's a great question. So, you know, the question from from Kampala is access to capital, which is the principal, you know, ingredient in a new business. What advice do you have for her? And how did you fund Shea Eileen when you first started? That's a great question. When I started Shea Eileen, I was in my 20s, so I had no money. And I had just finished Peace Score, as I mentioned. And so I really was poor. And I started Shea Eileen with part of my Peace Score readjustment allowance. And for the greater part of seven years, I self-funded. And so this was something that I had to put my own money in for a very extended period of time. And initially I had to leverage friends and family and, you know, get people to fund me from my personal network. And it wasn't until I'd gotten Shea Eileen to a point and initially I launched it as a 501c3 nonprofit. But then as I started learning about impact investing, particularly around using impact investing as a way to leverage and support businesses that were working in Africa, I decided to create Shea Eileen Health and Beauty LLC, which is right now the profit side of the enterprise that has received private equity funding from a small fund in New York based in New York called the Pan-African Investment Company.  And one of the things that I've learned in terms of funding is that people want to see what you've brought to the table. And funding is based a lot on relationships. And being able to get my first round of private equity funding was through the cultivation of a relationship. And so initially the advice I would give is, you know, leverage friends and family. You have to be able to put in a little bit of your own capital. And then of course look into resources like private equity funding. You can also look at crowd sourcing. There are a lot of different platforms to be able to raise money through online channels. You can also look at reaching out to. I know that there are different programs. There's the African Diaspora Fund, I believe, which is part of the diaspora marketplace that is sponsored by Western Union and the IDEA program. And so I think that capital is definitely a challenge. Again, initially you'll have to self fund, start developing those relationships that can put you in front of funders and then look at different types of funding like crowd sourcing, look at private equity and look at different ways that you can kind of first get your company to a point where you can get funding from larger sources. Thank you. That funding is it, isn't it? So let's now take some questions coming in online. I know we have a number of folks interacting with us through our social media. So the first question we're getting here is, can you describe how you overcame challenges with market access bringing Shailene to international customers? So there were several challenges. And I think the first one was making sure the product was good quality. And that challenge we had to address at the cooperative level. So the way Shailene operates, we work with women from the beginning of harvest season through production all the way to getting product to market. So when you look at our supply chain, we start very early in the process. And so initially one of the biggest challenges was ensuring that the women had access to the tools and the equipment that they needed to create a high quality product. And when you're trying to bring a product, even if it's a local, regional or international market you really have to look at the quality issues. And for being able to be successful in the marketplace, Shailene needed to have a brand and have a product that would be superior to other products that were in the marketplace. And so that was the first challenge, is really getting a high quality product. And then I looked at the marketplace. When you're trying to get your products to a particular customer, you need to know who your customer is. And in terms of knowing who your customer is, I looked at the marketplace and saw that a lot of Shailene products were being distributed in the U.S. market. However, there were two things that I noticed. One was a lot of the Shailene that was being brought to market was a chemically refined product. And so it wasn't a natural product. And the bulk of Shailene that leads the continent of Africa goes to Europe and Asia for chemical refinement. And so that was one issue that I saw. The second issue was I wasn't seeing women in the process. I wasn't seeing women in the marketing and the branding of products at that time. And so I started thinking to myself, well, who would be interested in a product that was 100% natural and two, that was sourced in a way that was sustainable and gave opportunities for these local producers to be able to generate living wages. And so from there I started identifying who that customer was and the profile of my customer. And that profile of my customer ended up being a customer that would shop at Whole Foods Market. And so now my third challenge was I've identified my customer. I know where that customer shops. How do I get my products into Whole Foods? And so you see the process. And I'm making it sound very linear. Of course, nothing in business is that linear. But my third challenge now was how do I get my great product into Whole Foods Market? So that customer that I've profiled can get access to the product and use the product. And this is where everything from my packaging, everything in terms of my pitch, getting in touch with a buyer, pitching to that buyer, those are the things that I had to go through in order to actually get the product to shelf. Yeah, no, so thank you for outlining that. I'm sure you, as an entrepreneur myself, I know it is anything but linear. So let's see if we can get another question coming in here online. So how have you funded your growth at the various stages of development? It seems like you're following shape production from the earliest stages, literally at the cooperative level. And so how have you funded the growth of the business? So initially the funding was self-funding. And so I used my own money. I then funded by reaching out to friends and family and saying, hey, I want to work on this. I want to create this great brand that can help the women who are producing this product. Can you help me? So I leveraged friends and family. And then as the organization started growing and as the company started growing and needing, you know, to get into Whole Foods, we needed to have more capital in order to grow and get the packaging and get access to marketing materials and doing a little bit of advertising and promotion. And from there, that's where I started kind of hitting the pavement and approaching different funds. So private equity funds, impact investment funds to get additional capital to be able to grow my business. And in the fall of 2014, after, I would say, a year and a half of going through the process, the due diligence process of working with a fund in New York, I was able to get my first round of capital. This is a very good question that's coming in right now from Milwaukee. It really goes to the point of whether entrepreneurs are born or are they made? Well, I consider myself an accidental entrepreneur. If you asked me in college what I would be doing, you know, 10, 15 years out of college, I never would have said I'm going to be running my own social enterprise, working with women and bringing products to market in a way that's sustainable and helping them generate living wages because I knew nothing about business. And so here's the thing, anyone who has these qualities that I believe I've been able to cultivate over the years, which is passion, persistence and commitment, you can become a successful entrepreneur. And it's not going to happen overnight. It took 10 years, well, seven and a half, eight years before I was able to get my products to market. And so it's one of those things where people, you know, they see the products and market and they hear the story and they're like, you must have been successful from day one. No, you're not going to be successful from day one unless even large companies and people we know, you know, like the Facebooks of the world, they weren't successful their first time. And so I believe that if you find something that you truly believe in and that you're passionate about and that you're very committed to and you, you know, outside of getting access to the skills, like over the years I've had to learn how to create a profit and loss statement. I've had to learn how to create a balance sheet or actually read and understand financial statements. And the thing is, is I started with absolutely no business backgrounds. I majored in political science and international relations and college and so I had no business background whatsoever. And I started in my 20s right after Peace Corps and so I didn't even have any business experience. And so for me, I believe, again, if you really have the passion for something, if you believe in something and if you have a great idea and a great product, you can be successful at being an entrepreneur. Thank you. And so here we'll get another question. This is from the Boaque American Cultural Center. How can we reach out to our elected officials so that they include the culture of entrepreneurship in college education? It's a great question, sort of, what can, you know, the government and elected officials do to really promote entrepreneurship early on in the educational process? Absolutely. I mean, for three years I was a mentor for entrepreneurs, well, young people, high school students in the Washington, D.C. area. And it was through a program called BUILD, and the program's objectives was to work with high school students from ninth grade all the way to twelfth grade and help them through those four years cultivate entrepreneurship skills. So we did everything from helping them come up with their idea, we helped them create their first business plan, we actually also helped them pitch to investors. And so that entire process allowed these young kids in high school, after they left high school, they had the tools and the skills if they ever wanted to create a business, they actually had that exposure very early on. Now, this was an additional program, and it was run by a nonprofit organization. So I think that question of how do we engage our government leaders to become more involved and to see entrepreneurship as something that is beneficial to young people. And I think the first step is approaching them. Here in the U.S., we approach our elected officials through writing letters. Now with technology and social media, it's even easier to get in touch and connect with your elected officials. I'm not sure in the different countries that everyone is at how things are set up, but I think the first approach is writing letters. You can leverage advocacy organizations in your local communities. I know with the groups that we work with in Northern Ghana, their local representatives, the women can approach them and talk with them. And so if you have that similar setup where you can actually go and talk to your MPs or your local elected officials, definitely go and talk to them, write letters, organize young people in your communities who are interested in entrepreneurship who think it's important, and get a collective voice that can approach these elected officials. Great. And I think the answer to this next question may very well be the participants of this live event. So what are the drivers for opportunity in African markets? So I think if I understand the question correctly, what are some of the different industries and sectors for growth? Yeah, exactly. So I would say, of course, agriculture. And I work in the agriculture sector. Shea butter is a natural resource that grows on a tree. And when we look at statistics where I believe about 80% of all Africans are involved in agriculture in some shape or form, I definitely think agriculture is an area that is not only a growth area, but it's one where you can impact the lives of people and a large percentage of people and impact it in a positive way if the proper supply chains are created. I also think manufacturing is very important and critical. And the reason why is a lot of African resource leaves the continent in the form of raw material. And so we need to start looking at businesses that are creating the ability for manufacturing to happen and for more value addition to happen in the process before products are shipped globally. So I'm a huge believer in looking at manufacturing, creating value added and finished goods before they leave the continent. In addition to that technology, of course, and I also think that looking at businesses and sectors, it's kind of a sub-sector, which is looking at youth and also women who I think need to be more involved in the business development process on the continent. I completely agree. How does the current business environment affect African entrepreneurs' potential? So I do think that there are many challenges, of course. You know, you can go... There's a gamut of issues from energy issues. I mean, I recently came back from Ghana. I was there for a few weeks in April. And right now the country is going through an energy crisis. And so, of course, that's a challenge for any entrepreneur.  And so I think that there are challenges in terms of infrastructure, in terms of energy, in terms of capital. That question was already asked. And I think that part of being able to address those challenges requires good governance. It requires engaging international organizations to look at these issues and look at ways to start addressing and solving a lot of these issues. And I think part of being on the president's advisory council on doing business in Africa, part of being able to give advice and recommendations, the 15 private sector leaders who are on this council, we're looking at these issues. How can we create a more enabling environment for entrepreneurs on the continent? And so I think that getting feedback from young entrepreneurs on the continent is part of that process, is to really engage young people on the continent and hear from them in terms of what are their challenges, whether they're day-to-day challenges, and how can not only the U.S. government provide a more enabling environment, but how can their governments as well? And I think that it's, for me, when I look at the work that I'm doing, I'm doing it from small rural communities, villages in Northern Ghana, and then I'm connecting products to markets in the U.S. And so it's hard, it's not easy at all, but I think that part of why entrepreneurship is so important to the continent is because if we're able to create strong businesses and if we're able to create businesses that are linking local communities to global marketplaces, I think that's the way that we can change the continent. Can't agree more. I think Ghana are the days of people investing in Africa merely for resources. I think it's clear this is, in many ways, the African century. Yeah. So Saddam Kisa Hussein asked on Twitter, Africa's economy is based on informal sectors. How can we shift that trend and still continue to improve our businesses? So I think shifting that trend, and I touched upon this a little bit, is being able to create more manufacturing opportunities. And so the informal sector, which I believe is, you know, when you look at the statistic that over 11 million young people enter the African job market every year, it's clear that there's a need for entrepreneurship because there are not that many jobs.  You see people on the street selling goods. And yes, they're part of the informal market. And I think part of looking at how to engage those groups into more formal markets requires so many different things from, again, I talked about earlier, you know, governance. There has to be political will behind creating certain policies that are helping to engage people more into formal sectors. And I think that education and knowledge, access to certain skill sets, part of being in the formal market, informal market is the lack of access to certain skills. And so being able to give people access to skills so that they can engage in the formal market is another way. And I'll just give an example. In Ghana right now, of course, you know, the oil industry is developing. And when I was there in April, one of the things I'm learning is that the areas where the oil companies are going, there is actually training people to be able to provide services to these oil companies. So whether it's, you know, hotel services, whether it's technology services, and without that industry and without those companies going there, you can't cultivate a more formal market. So I'm just using that as an example. And so that's where I think that the skill sets, the training, access to knowledge, all of those things can help kind of move from informal markets to more formal markets in a way where people are being more engaged in the process. Correct. Completely agree. Thank you for your great questions. Now let's check back in with our live audience in Uganda. Do you have another question for us? So one of the Mandela Washington Fellows at 2014, Martin Morganz is my name. You've spoken already for an agriculture as one of the economic drivers for Africa. And we all know agriculture itself is such a wide opportunity for African countries to get out there and make money out of it. But one of the challenges is the technology itself and stringent kind of roles on exportation. So with the agripreneurs that are coming up in Africa, mainly Uganda, Africa's food basket, what kind of ideas or innovations would you put out there for young people, especially young people that are coming up and to do agriculture to grow their businesses, especially using technology and export development. That's a great question from Uganda. If I understood the question correctly, it's really addressing the question of agriculture and how you leverage technology, particularly in the hands of young entrepreneurs to grow an agricultural business. Yeah. And so it connects back to what I was talking about before, which is manufacturing. A lot of agricultural products that leave the continent are in raw material form. I don't know if some of you saw the CNN report where in Ivory Coast the reporter went and brought chocolate, and the farmers had never tasted chocolate, yet they're cocoa farmers. And so if in terms of being able to expand and grow opportunities in the ag sector, I would say that we need to be able to see more manufacturing of finished goods. And so in terms of innovation, entrepreneurs, this is an opportunity to create chocolate companies and make chocolate in the country instead of exporting out the cocoa and then it's processed somewhere else, and then it's even brought back. And it's the same thing with cotton. Any type of ag product that you see, there's an opportunity for more value to happen in the countries of origin. And there's an opportunity for entrepreneurs and young people to really work together, I believe. Technology is very important, but I also think human capital is very important as well. Work together. You're in a room right now. You're participating in this program. Who's in the room with you? Who can you partner with? Who can you talk about these issues with?  If you really want to start seeing more benefit from the ag sector, it's about adding more value in country before products get to market. I can't agree more with the message of not going it alone when you're going to be an entrepreneur. So let's turn back to our online viewers and see if we're getting more questions from them. So an audience member in Port Lewis Maricious asks, how did you scale up? What were the methods you used to raise capital? It's a popular, popular question. Scaling, this is one of the things that I think is important before you can scale is you need to test your idea. You need to test your market. Do it small. When I started Shea Elina, I didn't go out and make, you know, 5,000 products. I made a handful, I made like 200 and tested it. And initially my packaging wasn't right. There were issues with packaging. So before you can scale, you have to understand what you're trying to scale. And you have to know enough about your market and learn from the lessons from a soft launch or a small launch before you can really grow and scale your business. And so some of the lessons that I took into going from making, you know, 200 to thousands of products was what did the customer like? What did they not like? Initially, I was only making one product. I was making just pure 100% natural-shaped body balm. And then when I brought it to the market, I got feedback that, oh, I would like this to be, you know, from some customers. We would like a cream. Do you have any creams? And so that's when I worked with a chemist to formulate a cream and then brought that to market and tested that. Again, in very, very small quantities initially. And how did I test it? I tested by doing events. I tested by giving out free samples. I, you know, I made small enough batches where I would be able to get that small batch to market, get feedback and then adjust and grow. And so in addition to testing my market, I also looked at what my projections would be after finding out that Whole Foods was going to bring us into their stores. And so that's where after testing the market, looking at my packaging, making adjustments, I was ready for my real launch. And this is where I needed additional capital to scale and to be able to get products into stores. And that's how I started looking at impact investment funds to be able to get the capital I needed to grow the business. That's great. And I think you underscore something so important, which is not letting perfect get in the way of good. Yeah. Better get a good product in the market and get market feedback before you commit and build up stock and inventory. Absolutely. And this is where too having mentors is important because again, when I started Chaelene, no business experience, no money. I was in your shoes and it took me a while and maybe longer than most, but I still, you know, I was committed to it and getting a mentor who knew the Whole Foods market and who actually worked at Whole Foods to give me advice on packaging to give me advice on, you know, how to make certain changes to my product line was really important to help me scale.   All of that is part of being able to successfully scale your business. Great. An audience member from a viewing group asks what were the challenges you face as a woman entrepreneur exporting to the U.S.? Hmm. The exporting part was actually pretty easy for me. And I do think part of the reason why is I am an American citizen, so part of it being able to, you know, take advantage of certain programs was helpful to me. I didn't have issues exporting as a woman. I think more issues as a woman, some of the challenges I've dealt with more is being taken seriously in certain environments, certain business environments. People think that I'm younger than I am and at times being young or, and when I started my business I was young. You know, people don't take you seriously at times and I think that there are certain challenges that women deal with that men probably don't have to deal with. And I dealt with those challenges simply by getting a very thick skin and not letting things bother me and making sure that I had the right people around me who could balance out some of the challenges and the issues I was facing as a woman. You know, unfortunately we do live in a world where there are gender inequalities and we just have to deal with that, but we shouldn't let it hold us back and I think that if you are confident in what you're doing and if you're confident in your abilities and you can get confidence simply by practicing, simply by doing, simply by putting yourself out there, you can face a lot of the issues that come from being, you know, not taking seriously as a woman in business and I think that as you become more and more successful at what you do you will garner the respect that you need to be able to run your business effectively. But in terms of exporting, I want to point to AGOA because I think that the AGOA program, the African Growth Opportunity Act is a program that each and every one of you should be familiar with, should be aware of because it's the largest policy program that is supporting trade between the African continent and the U.S. and so there are a lot of resources through AGOA that can help you as you're trying to do exporting and as you're trying to bring goods into the U.S. market. Wonderful, thank you. Courage, eternal youth and shattering ceilings are byproducts of Shayleen's Shea Butter, right? So an audience member in Mauritius is also asking, how long did it take to get your products to be certified and to start export to the United States? What were the some of the regulatory and sort of export hurdles that you had to overcome? So since I wasn't exporting or out of Africa importing into the U.S. food product, the process was slightly different. With food you have to go through a lot of certifications because I was using Shea Butter as a skincare ingredient, I didn't have to go through a lot of those certifications. And so for me it simply was making sure I had the right harmonization code making sure that when you export out you need to make sure you have the right data in terms of where the product is coming from, who's sending the product, who's receiving the product. I work with different freight companies and so I kind of outsourced all of that to the freight companies and when I bring the product in it has to be signed off by the FDA and since it's being used in cosmetics essentially they just check the product and then they sign it off. If you're bringing in a food product there's a long list of different certifications and different regulations that govern food and so I would advise you and I'm sure that at the embassies that you're at right now they can give you the contact information of where to look when you're looking at food imports because it's much more challenging and depending on what country and what product there are regulations around that as well. Let's turn back to our live audience in Kampala to get another question. Asha Ali is my name, part of Generation Change 2.0 Developing businesses in developing countries have to face numerous challenges like poor infrastructures limited access to funding or high interest rates. As a result of this developing countries have a number of numerous informal businesses which do not pay taxes, do not have a legal payroll or do not are located in facilities that are not legally registered. Entrepreneurship is the most effective way to reduce poverty and generate wealth but given these challenging environments and high levels of informality how can we develop policies that reduce transaction costs and foster entrepreneurship? What a great question and I think really is looking to how do you overcome a lot of the development challenges that you may face in a lot of developing countries while at the same time you're trying to grow your business overcoming infrastructure hurdles, lack of capital, informal economies what advice would you impart mainly looking at the cooperatives that you're working with and part of the production process? I think for me I've been able to address these challenges by developing really strong relationships on the ground and so yes in the communities that we work in we've had to create facilities where we're actually bringing electricity and water to that community because the infrastructure doesn't exist now I know that a lot of entrepreneurs that's a challenge you can't just bring electricity and water to every place that you're working in but we're in a great position where we're able to do that but I would have to say the success that I've been able to get in terms of working with the cooperatives has been because of the leadership of the cooperative members and the women that we work with who are amazing and they do incredible incredible stuff and having strong leaders on the ground has been very very beneficial to my business model. In terms of policies and developing policies again I would go back to this idea of really understanding what the challenges are because we can talk about the challenges right it's capital it's infrastructure but what are they exactly and what about the infrastructure what about capital preventing young people from being able to become better entrepreneurs from taking people in the informal market to more formal markets and this is where being able to have people on the ground have the right conversations to be able to feed into policies that they can ask their governments to develop and implement and so again depending on what country you are there are different processes and depending on what the issues are you might have to engage advocacy groups the civil society you might have to engage the diaspora so those are all the different resources that I think can be beneficial in helping to develop the right policies but if I had started Shailene and only thought about the challenges I probably wouldn't have started Shailene and this is where I think it's more important and I'm not trying to be you know head in the air idealistic because I do know that there are serious issues but think about know that the challenges exist but more importantly think about what you're trying to change and think about what is important to you what you're passionate about focus on that that's what I focus on again I had no idea what I was doing when I started but I didn't think about the challenges there are so many challenges that will come and you'll figure out a way to address them you know for me I didn't have to deal with the challenge of figuring out how to get the shea from northern Ghana to the Tema port why? because there was someone on the ground that I trusted who knew what they were dealing and they were able to help me navigate that and so that wasn't one of my challenges getting products from Ghana to the US wasn't a challenge for me but it might be someone else's challenge and then you have to deal with that challenge when it comes up and so that's what I would advise and then of course always appeal to your local governments always appeal to your governments to make policies and decisions that will be more beneficial exactly audience members from our viewing group in Mauritius ask as a leader what is the number one question you would ask all the times to achieve mission and vision of the company how do you integrate a global mindset and cultivate continuous innovation in a company so for me being Ghana American has been huge in terms of my concerns of the world in terms of what I value what I think is important and the development and creation of Shailene really stems from my African roots and I think that every single person who's participating in this program your number one asset is the fact that you have African roots is the fact that you're in Africa and sometimes a lot of times we don't take pride in being African we don't take pride in our roots but honestly that is your asset and so for me because of the fact that I come from Ghana is why I created Shailene because I connected to the lives of shape producers and I connected to the challenges and the issues they were dealing with and I saw an opportunity despite those challenges to address those issues in a way a sustainable business model that is the core of my business that is why I get up every single day and when it comes to your question about how do I maintain that vision and that mission in my company it's because I started it from that perspective that is the foundation of Shailene and so every day when I get up and when I work and I whether it's talking to a buyer whether it's talking to my team members and my staff we always go back to is the work that we're doing in line with the mission in line with our core values and you can develop your core values our core values, transparency empowerment, quality those are our core values what are your core values the question you should be asking yourself is what are your core values as you're starting your business what are your core values that regardless of where you look in your company or in your enterprise that is consistent throughout quality, empowerment transparency and so those are the things that we look at every day and that we work towards achieving some days you'll be perfect at it some days you won't be perfect at it okay I like you'll never be perfect at it but you have to keep going but it's worth trying the question coming in which is I have an ice cream and pastry business even though I don't know much about pastry making how can you find a staff that is qualified and trustworthy when you as a boss are not an expert and can you successfully lead a business if you have another job on the side great question I worked several jobs on the side before I was able to transition to shailing full time the latter part of your question is yes you can you just have to have really great time management and for me I worked a full time job for four years in addition to building shailing and then I stopped working full time and just started doing part time gigs here and there so I could have control over my time and so my process to going from start up to business real business is required having to work other jobs and required having to work full time so I think that's the normal part of the process in terms of not being an expert at something this is where technology the internet I think can play a huge role anything I did not know when I first started I would just research Google I would go on and I would put in my question where can I find caps where can I find labels where can I find a designer and I just built my business with no knowledge simply by going into on the internet and researching things and then I wouldn't just pick the first thing and go with it I would compare what different sites were saying and I would also compare the credibility of the site not recommending just going online and taking anything you see online you know go to credible sources go to universities go to see what people are reporting on I didn't know anything about Shea Butter and so I would Google reports that either were coming from a governmental organization or coming from another company or coming from a study and that's how I learned everything that I've been able to to accomplish was you know I don't have an MBA I didn't get any experience with business I just learned by researching and so you have that ability if you have access to internet and I think most of us these days have access to internet and so some of the questions you should be asking is you know what is the equipment I need for pastry making what are different ingredients that I can use and as you start learning when you bring in someone on your team who has more knowledge of the it's always good to have someone on your team who's an expert you will not be an expert at everything even though I can do a profit and loss statement in balance sheet do I enjoy it can I do it quickly no that's why I have an accountant that's why I have a bookkeeper so don't be insecure about having someone on your team who might know more than you learn from that person and you can always compare what they tell you against what you research that's true and that's really important because you want to make sure that you know your business like the back of your hand you want to make sure that whatever product or service you're bringing to market you are an expert about that product and service so now take the time as you're working a full time job and you're starting this pastry company that gives you the time to really learn about how to run a pastry business to really learn about how to get the ingredients that you need you know what are the different equipment that you need all of that stuff so give yourself that time to learn bring people on who are smarter than you but who are willing to collaborate and work well with you and when it comes to staff and finding the right staff is more important than what looks good on paper because you can find someone who has so much great experience I've gone through this who's had hired someone who had 20 plus years more experience than I did she was older than me and there wasn't a good fit we couldn't work well together we were both very nice and cordial but our personalities didn't work well together and so fit is very important of course you want to find someone who has the skill set and the experience but you also want to find someone that you work well with that you respect there's mutual respect that you understand each other's communication styles those soft skills are also very important when you're trying to build the right team so I guess the takeaway is if you're an aspiring entrepreneur or running an established firm it's important to know what you don't know yes absolutely so now we'll go back to another question coming in online which is how do you start a company in a place where policies are not helping young entrepreneurs well it definitely depends on what the policies are but policies I think there's this is a little bit more challenging to answer because I'm not sure where was that question coming from it's coming from an online viewer policies have their place but at the end of the day policies only come to life when people use them and so starting a business unless there's a policy where you can't start a business or there are huge kind of challenges and barriers to starting a business I would say start your business anyway and try because at the end of the day if you let external things prevent you from starting something that you believe in how will you be able to ever challenge or address those external factors and that's the way that I look at policies and the way that I look at certain systems if I looked at for example the marketplace and saw there was like a million different shade brands companies I would have said to myself there's no point in starting this there's no room for me the market is too crowded but I really believed in what I was doing and so I started anyway you're not going to have all the answers it's not going to be perfect but when you start it at least gives you a place to kind of launch from and it depends on the type of business that you're trying to start more importantly than the policies that are preventing you from starting your business which is a hurdle which is something that you might have to address earlier or later on I think more importantly than the policies is really understanding the business that you're trying to start and seeing how you can either go around some of the challenges or address those challenges directly but if you don't start it doesn't matter if the policies exist don't exist another example of that is to look at the policy like a convention and many entrepreneurs are disruptors they're coming into an established market taking established conventions or policies and breaking them so hybrid engines once upon a time the only policy for a vehicle was the internal combustion engine and fuel and today you can see that convention being broken around the world and Africa the advent of mobile money is really shattering all kinds of conventions across all kinds of markets so there's a lot of opportunities to overcome obstacles as opposed to looking at them as something that's stopping you as an entrepreneur so an audience member in Kampala asks how can small firms in Africa survive in today's competitive market environment? know your customer um you know I know who my competitors are I don't focus too much on my competitors I focus more on what I do very well what differentiates what Shayeline is trying to accomplish from other competitors and I focus on my customer and so for me it always goes back to your customer so understanding your customer profile and being able to build a lawyer customer base is very important to any business regardless of how competitive the market is and so I think that you know Shayeline is a small business you know we're going up against companies that have been selling Shay Butter for 20, 30 plus years we're we're successful in the marketplace and it's because we know who our customer is and so that's the advice I would give is know who your customer is if you're selling a great product or providing a great service and you're connecting that product and service to the right customer you can build a successful business thank you I know that sounds very easy it isn't but the first step is really knowing who your customer is right can't agree more so we're getting a great question on workforce qualifications from in my view one of the more qualified countries in Africa from Morocco is a sub-Saharan African workforce qualified I mean I think it depends on what your definition of qualified is I do think that for example in the communities we work in the women are not formally educated a lot of the women that we work with cannot read or write and so you would you know if your definition of qualified is being able to read or write then they're not qualified however they can learn and you can pass on knowledge and you can pass on skill sets even though they might not be able to achieve certain things from a more traditional idea of qualification or traditional idea of the need for formal education they're qualified because they have a skill set they create an incredible product they take oil from these seeds and we can connect it to the marketplace so again it depends on how you define qualified and if you have access to resources and if you have a skill set yes you are qualified you can always improve and grow upon your knowledge and this is where having access to training you know is really important being able to give the workforce opportunities to improve their skills is always very important but that's not just in Africa that's everywhere and so I believe yes you're qualified and if you have access to the right tools the right resources the right training you can do much more with the resources that you're given and so many of the greatest entrepreneurs we know of are folks who walked away from the best universities didn't get a formal education and they just harnessed these other cultural aspects to entrepreneurship no fear of failure and many of the things you've discussed before we close I'd like to hear your final thoughts and anything you'd like to leave with our viewers today well first of all I'm very excited that you're all looking at entrepreneurship and you want to start this entrepreneurial journey I'm 110% behind this it's going to be challenging you will experience some failures but honestly it will be the best thing you've ever done because it will help you to grow as a person it will help you connect to the world in a much more authentic way because you're pursuing your passion you're pursuing what you believe in and the last thing I would say is think big but you'll be taking small steps so true so true so thank you all very much for your fantastic questions that wraps up our live event for today Raham I'd like to thank you very much for joining us thank you finally I'd like to thank our live audience as well as all of you who joined this program live from around the world my sincere thanks to the viewing groups in Port Louis, Siddharah Salam, Rabat IRC, Arbijan and Addis the recording of this program will be made available later on this page remember the 2015 Global Entrepreneurship Summit is happening in Nairobi, Kenya on July 25th and 26th it will be the sixth annual gathering of entrepreneurs at all stages of business development business leaders, mentors and high level government officials for more information visit www.ges2015.org stay tuned for our next interactive program thanks again and see you next time


OK, hi, my name is Eva Cintic, sem lekturer for the course of real analysis, so this is my email, so I am currently research scientist at the University of Nova Gorica, which is in Slovenia, just behind, through the border, but I'm Italian and so basically the main, I would like to outline the topic of this course. Oče vedeljamo, da je častak, častak, častak, častak – nekaj najbičaj pri Sobo-Amplijnev skupite. Se nam izop revi verbila del, da sem daji izop vredila kaj distinguishanje in učinjanje, načo ne kadunje, nič je nekaj površal. In, nekaj, častak, častak, častak, častak, častak, častak, Ok, maybe some of you already studied this subject, do you already know this? No, no, I mean all these things, have you already? Ok, ok, in case it will be a repetition. All this argument will be carried over in one space dimension, so we know. I will recommend you some book, so the book of Reuden, which will be somehow the book that I will follow, so real analysis. Basically we will study the chapter from three to chapter six of this book. So you will find some copy in the library here, ok. So another good book is the book of Reuden and Siegmund. So the title is measure and integral. And finally a very classical book, maybe a little bit tough, but it's a good text, book of Reuden. It's real and complex analysis. Reuden, yeah, it's an H and Siegmund. These are two authors. So as I told you, somehow the main topic of this course will be the Lebecki integral, which somehow the aim is to extend the notion of Riemann integral and especially to extend the class of functions which are integrable. And this also will require to introduce the domain on which this function are defined, ok. So just to give you, before starting with giving the definition and the notion, I will just somehow motivate why we will need to enlarge this space for instance of continuous function. So for instance, consider a function f in a just closed interval with values nr, a continuous function, ok. So in consider the integral, you can think about it as a very elementary notion of integral, as for instance the Riemann integral. And in the most elementary case, you can think about it as the area between the graph and the x-axis, ok. So we shall see that this notion will be not enough when you deal for the application to ordinary or partial differential equation, ok. So we will have to enlarge, because when you deal with application with PDE or ODE, you will need to somehow to define a norm which is defined by means of an integral, ok. And also what you need is that the space which is defined with this norm must be complete, ok. We will see that if you define for instance the space of continuous function and though the space of continuous function with a norm which is defined by an integral, this will not give you a complete space. So a space which is not complete is not very useful for application, ok. And by somehow we will need to enlarge the set of the function, ok. Ok, so, ok. As I told you, consider this norm. So defined in a very simple way. Ok, you have f is continuous, so the modulus, the absolute values of f is still a continuous function. And it's easy to see that this function is a norm, ok. Because it's not negative, it's zero if and only if f is zero. If you multiply it for a constant, the result will be the integral times the absolute value of the constant and the triangle inequality also, ok. This is very easy. Ok, so, no, we, and though the space of continuous function domain defined in AB with values in R with this, with this norm, ok. Ok, of course, starting from this norm you can always define, you can always define a metric, ok. Take the difference between f minus g. So, as I told you, as I already anticipated you, this definition of the metric will not give rise to a complete space, ok. And we need completeness in the application because usually you have to pass to the limit so you want that good property must be precept when you pass to the limit, ok. So, ok. I recall you that a metric space is a space which has this property if you have a Cauchy sequence, it converts and the limit has to belong to the space itself, ok. So, now I will just briefly exhibit a sequence of continuous function whose limit does not belong to the space of continuous function. So, I just will introduce this sequence of function by the graph, which maybe is the best things. So, you have your interval a, b. So, took a point in the middle, for instance point c, and then took a point c plus 1 over n and consider the function f and the finite as follows. So, this is the root, the y axis, for instance. So, is 0 between a and c, here is 0, between c plus 1 over n and b is equal to 1, ok. And here is defined by a fine interpolation, ok. So, probably the analytical definition should be this, just to be 0 between 4x, between a and c. Here should be nx minus cn when x is in between c and c plus 1 over n n is equal to 1 for x between c plus 1 over n and b, ok. Ok, so, this function is continuous because the values at c and c plus 1 over n matches if you take the limit on the right and the left. Ok, so, let us first check that this fn is a Cauchy sequence in the metric that we just introduced, ok. Ok, just I will call you the definition of Cauchy sequence. So, we have that for any epsilon positive, there exists an index n bar such that for any n and then written n bar we have that fn minus fn fn is less than epsilon, ok. Ok, then consider for the computation, for instance, consider that n, ok, for computation just to fix the idea. Assume that n is larger than m and we want to estimate fn minus fn which by definition is nothing but the integral between a and b of fn minus fn. Ok, we can, of course, we can split this integral in three parts. So, the part between a and c of fn minus fn c plus fn plus 2 plus 1 over m and b fn. Ok, so, basically, you have that this is 0, this part is 0 and this is less than 1 because we are both like this. Ok, the drawing is not the best but you understand. So, this is basically less than 1 over m. Ok, so, it's enough to take n bar larger than 1 over epsilon and you got that, indeed, fn is a Cauchy sequence so this is a very easy result. Ok, but now we want to prove that fn does not converge in the space of continuous function, ok. So, we argue by contradiction. Assume that, so, by contradiction, assume that there exists a function, a continuous function belonging to our space and such that we have that fn converges to f in this null. So, we will see that we will reach a contradiction, ok. So, what we would obtain. So, you consider AC of fn minus f which, of course, is less or equal than this which is precisely the norm that we are considering. Ok. Ok, but we know that fn is identically zero in AC so what you get is that AC depends to zero, ok. Of course, this does not depends on n so this means that this is zero and so this means also that the integrand is zero because it's positive. So, in this piece of the full interval, ok. We consider the other part of the integrand. We consider the part between the last part. So, c plus 1 over n B of fn minus x which again can be bound by the fully integral and this we know is zero by our assumption. Ok. Ok, but we know that here fn is equal to zero suit one, sorry. So, you get this. Ok, here you have that the left hand side integral depends on n but we know that the integral is continued with respect to the end points. So, what you get is that this converts this converts to cB. So, at the end what you get is that cB minus f is equal to zero. So, again by the same in analogous argument you have that f must be identically one in the integral cB. So, at the end what we found is that if f is the limit f is like this so it's zero in AC and this is one in cB which of course tells you that f is not continuous, ok. So, we reach at the contradiction. This means that probably the continuous function is not a good space where to work, ok. Ok, so we need to enlarge this function space and so the first way to do it will be to somehow to enlarge the domain in which those functions are defined, ok. So probably just interval or or elementary set are not enough. So tell me if I so the way to enlarge may arise now or the way to enlarge this space function is to introduce indeed the Lebesgue integral and to introduce the Lebesgue integral we have first to introduce the Lebesgue measure, ok. So you have to think of the Lebesgue measure as somehow at a generalization of the notion of length for intervals, ok. Ok, so I will first introduce some terminology which is probably very easy but just to do it right from the beginning so what do we mean as an interval. So these are intervals so this would be a closed interval this would be an open interval and then you have half open and half closed when you have this situation, ok. And then you have these are bounded intervals and then you have also the offline interval and so on the left you get closed and so on so you have minus infinity B and minus infinity B. So we would like, as I told you to give this definition of measure of Lebesgue measure in such a way that it extend the notion of length and moreover I will list now some property that we would like Lebesgue measure fulfill. We will see that will not be possible that to find a measure that fulfill all the four properties that I will list. So we will be content with just three of them. We have to choose some. So the first one that we would like to have I call it the zero property is the following we would like to have a measure so asset function which will extend the notion of length which will be defined on the set of parts of R with values in the set of the extended real numbers. So PR is the set of parts set of parts which is just the collection of all the subset of R is the subset of R and it contains of course also R itself and the empty set. And this it is we will call it the extended real number. Yes, yes it could be plus infinity. If you think as I told you, the measure that we are going to construct will extend the notion of length for integral. For instance, if you have to compute the length of this interval it will be plus infinity. It's infinity the length. So of course we have to include plus infinity also here. So this is somehow the first property the zero property and we fix the domain and the co-domain that we would like to have. We will see that this is too much to require this. We will have to restrict the domain but we will see later on. So the second property or the first property property 1, let's call it property 1 is what I repeat is that we want that the back measure coincide with the length of an interval for any for any interval. As I told you we can see we can consider the empty set as a degenerate interval of measure of measure zero. This is just a brief remark. So the second property that we want is very crucial because we want to to have good property when we pass to the limit. Because in the application you always pass to the limit. And this would be translated in the requirement that we want that the countable additivity property so what does it mean? It means that if you have a collection ok in set of parts of R of this is a sequence of these joints there must be these joints this joint set then of course for which M is defined ok then what you want you want that the union of the countable union of this E n must be just the sum of E n of course they have to be these joints because otherwise and ok so the countable this is just brief maybe trivial remark but of course this countable additivity property immediately implies the finite additivity property that says that of course if you have this also this will also if you have A and B two sets belonging to the set of parts of R and A and B is joint then you have that also the measure of A union B will be just the sum no? as you can see it is just defining E1 equal A E2 equal B and then E n equal to the empty set 3 because we require that ok this is just an easy things but just to just to fix the idea and then we want to have another somehow geometric property to be fulfilled quite intuitively so we want that M is translation invariant so or namely we are requiring that the notion definition of measure will not depends on the location of the set this is trivial for the interval but we want to be preserved also for this extended set ok so let me write it more so basically we have a set E in a set of parts of R and you define take one one element Y in R and you define E plus Y which is the translated set with respect to Y which is X plus Y X belongs to E so what we want is the measure of E must be equal to the measure of E plus ok so we will see that it is not possible to have a set function M that satisfies all the four property ok so the third one the last one no we cannot get rid of this because it's this is too important it's very intuitively M shouldn't depends on the location what we could do is to replace to relax the second one in the sense that instead of requiring the finite additive property ok in this case you won't reach a contradiction but it won't be useful for application because as I told you we want to have good property when you pass to the limit so we have to to maintain this this one of course no because we started by motivated by the fact that we want to extend the notion of the length so what remains is to relax this so somehow we will have to reduce the domain of this set function so we will be we have to be content with somehow a subset of the set of parts of R so we will call this subset has the set of the back measurable set and we will see that this is indeed we see a true subset of the set of parts of R ok so let me so basically now the aim of of the first lecture of this course will be to construct a set function which satisfies the properties one two, three and to define a good domain for this for this function ok ok so we will see that it would be convenient to define the domain of M in a way that it is a sigma algebra ok maybe you already know what is a sigma algebra did you already study yes ok but I will recall you again so you have that give you a definition so you have that given X ok I mean still stuck on the real line setting somehow so you give a set X and you consider A as a subset of the set of parts of X so we have that A sigma algebra if you have these three property so you have that the empty set must belong to A second one is that if A is a set that belongs to this italic A if you want then also the complement of A belongs must belong to sigma algebra and finally if you have a sequence of set A n such that A n belongs to A then you must have that also the countable union of A n must belong to to the sigma algebra so we will construct M the domain of M in this way in a way that it would be we show that it is a sigma algebra ok just a brief brief remark you have that probably you already know that the morgan's law ok from that also the intersection the countable intersection of this set belongs to the sigma algebra because of this union ok, so you do operation that still allows you to stay in the set of in A ok, and now I will introduce another definition ok, so we shall say that M is a countable additive measure ok, if it is ok, a non-negative of course value ok, whose domain of definition is a sigma algebra algebra call it this italic M M of sets such that ok, we have that these two properties are satisfied so the measure of the empty set is zero and then we want the countable additivity property because we call it a countable measure, so we want that for any sequence in the sigma algebra of this joint set of course we have that so what we want that the measure of the countable union of this E n must be just the sum of the measure of the E ok, this is the definition of countable additive measure, which somehow embodies all the requirement that we that I mentioned before not all of them but we still want to have that to construct a function like this, so a countable additive measure, which in addition also is translation invariant ok and and preserve the notion of length ok, so now what we want to do from now on is the following task so we want construct a countable additive measure which is translation invariant and such that preserve the notion of length ok for any ok, for any interval interval yeah, yeah will be defined on set of R on subset of R, yeah and we will call this I mean the domain of M as I told you we will define, will be the back measurable set and we will have values on the extended real line ok, this is why high set that is non-negative so it is from zero on and as values in the extended real line so it is ok we will start to construct this such a function and to do this we will need first to introduce the notion of outer measure ok, so finally we will define somehow this is an auxiliary definition and we will pass through this definition in order to define our back measure ok, so you consider a set A in R and then just think about a collection of open intervals which cover A ok so ok, first of all of course A belongs to the set of parts of R this is trivial and consider accountable collection ok accountable call them IN of open intervals which covers intervals which cover A that A is contained in the union of of IN so consider interval because for the same reason because we know how to deal with interval we have the notion of length so we have a starting point ok, so for each such collection you consider the sum of the length of this interval ok and you define as outer measure so we define outer measure in such a way we have an outer measure and it is M star ok in this way this will be a set function which will be defined actually on the set of parts of R so later we will restrict this with values in the extended real line and so we associate to a set A these values so will be the infimum of the sum of the length of IN where IN is a set in the collection of open intervals which cover A ok, this is a definition ok, just some some remark ok, so we have that the length of the interval of course are non-negative number so this sum is well defined so it doesn't depends on the order in which you sum we are not talking about the empty set because of course at least we have R which will cover A for sure ok, so this somehow it's a good definition ok, now we will we will list some property of this outer measure ok, some really easy easy property ok, so it follows that so the outer measure of the empty set will be zero of course ok because ok, you can think as a particular collection as the collection of of the empty set which can be understood as degenerative interval ok ok, then you have ok, monotonicity property or namely if A is contained in B then you have that the outer measure of A is less than the outer measure of B so why this? so you can so actually when you consider this you are considering a bigger bigger set, so the infimum in principle would be smaller ok follow from definition from the property of the infimum if you are doing the infimum in a bigger set of course what you will get would be smaller or equal ok, so just to ok, I just write this because to be complete, but of course it's easy, this is because when you consider this collection of IK IK which covers the collection which covers B this is a subset of the collection of the IK which covers R so then you get property of infimum you get the tazis, ok ok, then ok, another easy things is the following try to raise ok, each set consisting of a single point X has intermeasure 0 and it can be easily seen by the fact that of course you have the single point set X so for any epsilon this this set is contained in this symmetric interval and the length of this interval yeah this one IK and this one the same are contained, yeah I mean, you can use them to cover A, since A is smaller than B you can use them to cover ok yeah, it's the converse so A is contained in B but all the collection which covers B will cover also A so when you you do the infimum of this this will be bigger than the infimum of this, ok yeah, it's the reverse ok and so this is of course to epsilon so since this is true for any ok, already for any epsilon you can make this length arbitrary small so this is we get of this single point set is 0 ok, these are easy things ok, now at least we have defined this notion of outer measure we just list some quick consequence of the definition ok, now we will prove a proposition that tells you that the outer measure did extend the notion of length which somehow is what we want ok, so the outer measure of an interval is its length ok ok, to prove this claim we will argue by step ok ok, we will start by considering a closed bounded interval and then step by step we will extend the notion, ok so we will start with the case the case I equal closed bounded interval ok, one way is quite easy in the sense that ok, you have that for any for any epsilon positive you have that the corresponding open interval A minus epsilon B plus epsilon we have that cover AB so you can think about as a set in the definition of outer measure so we have that m star AB is less or equal than B minus A plus epsilon this is for any epsilon and this is follows from from the definition and so as usual since this is for any epsilon we can this is preserved this must be true even when epsilon tends to zero ok, so at least we proved one one side of the of the equality, we want to prove the other one, which would be somehow more tricky so now what we want to prove is this ok, now again we recall the definition of outer measure and we observe that this would be equivalent to prove another fact, so by the definition so by the definition of outer measure which in turn is defined by the notion of infimum ok, we have that it is equivalent to prove to prove that if you have accountable collection if is accountable collection of open intervals which covers AB we have that the sum of the length of IN which is precisely the right hand side of the definition of of outer measure is larger or equal than B minus A and I call it star for any such a sequence this will be preserved by the infimum so at this point we will make use of the unborel theorem ok so somehow it would be better to deal with the finite sequence now it would be easier so this is why we will use the unborel theorem the unborel theorem we have that ok, that any collection of open intervals which cover, covering AB contains finite which is which is what we gave so we pass from accountable collection from finite collection finite subcollection which also cover AB and of course it would be enough to prove star for this finite subcollection ok because the sum of the length of the finite subcollection would be no greater of the sum of the countable collection ok just just to be enough to prove finite subcollection so basically we have that q is contained in the union of a finite ok, so we have that since the closed interval is contained in this finite subcollection so of course we have also that element A which belongs to this closed set must belong to this union of course ok, from this there must be must be one ends which contains A ok, and let us call let us denote such an interval as as A1, B1 ok ok, then there are two cases the good one is that if if B1 is larger than B then we are done, that is nothing to prove ok, otherwise we have to continue with our argument, so if on the contrary B1 is less than B that is what we call then B then we have to continue then we have that B1 belongs to AB so, and since B1 does not belong to A1 B1 open there must be another interval an interval A2 B2 belonging to this subcollection of course because we are speaking about open interval ok, so there must be an interval A2 B2 always belonging to the subcollection in the finance collection ok, such that B1 belongs to A2 B2 and so we have something like this A2 B1 B2 and also here, A2 B2 is larger than B, then it's ok it's a good case otherwise if B2 is less or equal than B we have to continue with this argument and so if we iterate somehow this argument what we get we will find a finite somehow we get a finite sequence of open interval belonging to the finite subcollection ok from the collection ok, such that they are placed in that way you have A AI BI minus 1 and BI something like this ok, this is enough ok, so the thing is that since our subcollection is finite this process must end at some point this is why we end up with some finite sequence of interval ok and somehow this process is over so the process is over when the endpoint B belongs to the open interval AK and ok ok, so finally what we get we have that the sum of the length of IN is larger or equal than the sum of the length of AI BI this I mean in the finite subcollection these are this this interval that we selected somehow so this is equal to what this is a kind of telescopic sum plus we have BK minus 1 I mean it's not a telescopic sum but you will see some ok, so if you sum up in another way no B B1 B1 A1 so if you observe this you have BK you collect this term AK minus BK minus 1 this is negative and then you have minus AK minus 1 minus BK minus 2 which again is negative minus A2 minus B1 minus A1 so at the end you get that all this stuff here is larger than BK A1 ok, because this is negative but you have a minus in front ok, which is of course is larger than B minus A ok, so at the end what we found is indeed the inequality star that we were looking for larger than B minus A so somehow the statement the thesis follows for for the interval for compact interval the thesis follows for I equal to AB so now we have to extend this equality to the other kind of interval for any finite interval but you have to deal with the opening interval and this measure is B minus A and then the close interval from A to B is there is Julian's union of 3 sets the single term A, the single term B and the open interval from A to B from the counter of this Julian's property you can see that M star of the problem from A to B equals 0 plus B minus A equals 0 equal B minus A I mean I'm not maybe we can discuss later I don't know if you use the countable what do you use, the countable additivity property for what, for length or for what I did not get your maybe we can quickly discuss later because now I can if I don't see the things written I cannot follow okay now we have to extend the proof for so we use what we prove so far to stand this equality for any bounded set any bounded interval, sorry if I is any finite interval then you get what I want to do is that given any epsilon positive there is a closed interval called it J okay, such that J is contained in I and the length of J can be controlled from below by the length of I minus epsilon okay, hence what we get okay, you have that of I minus epsilon is less than the length of J and this is equal for the step before is equal this is step probably I call it A this is step B J J is contained in I okay and this is less or equal now you use the monotonicity property of m star of I less or equal to m star if you want again for the monotonicity property of I, the closure of I which is equal of the length of I closure which is equal to the length of I so we know that this holds for length since this is true for any epsilon positive you get that indeed the outer measure of I is equal to the length of I okay and because it's in between these two so finally what remains to prove if infinite interval then you have that real number find a closed interval J contained in I such that you have that the length of this closed interval J is equal to this arbitrary large m okay as you have m star of I is not equal to m star J okay since this is true for any m then any n positive of course then you have that m star of I equal to plus infinity which is equal to the length of I so with this we conclude we span all the cases we consider all the cases we conclude this proof so the last minute okay just anticipating what we will prove tomorrow okay so tomorrow we will prove the following we will prove the countable sub additive property for the outer measure so this is composition so you have an countable collection of set you don't need to require them to be disjoint because we just get what we get is so weak that we can also take them as any countable collection so what we will prove is that the outer measure of this countable union will be less or equal of the sum of the outer measure of an so for the outer measure we just be we just be we just obtain this less or equal not even if we require a countable disjoint set we cannot we have somehow to restrict the set that we so we will have to introduce another notion of measure okay so this is the sub additive okay sub additive property okay and then okay in the last minute we can just introduce some terminology but tomorrow I will recall you again so we will note with this italic g the collection of open sets of r with the with this italic f on the core where is the closed set with g delta okay the family let's call it the family of sets obtain it as countable intersection of open set with f sigma the family of set obtain it as countable union closed okay so somehow the idea the reason why we introduced this family set is that this somehow nice set easy set set that you can imagine would be to approximate the measurable by means of this easy set treatable set so would be very useful for us to see that you can approximate in some suitable way the measurable set by means of a set pick it from this class of set from this family okay thank you


Take a minute and sketch this example in your notes. Did you do it? Is it sketched in there? Good. Alright, so we want to find angle 1 and angle 2. Angle 1. Angle 1 is an exterior angle to triangle ABC. And as a result, I know that the exterior angle theorem says 1 is equal to the sum of the two remote interiors. Now the two remote interior angles are the ones that don't touch angle 1. In other words, the two remote interiors would be 35 and 25. So once again, the exterior angle theorem says angle 1 is equal to 25 plus 35, which makes 60 degrees. Lastly, we need to find angle 2. And angle 2, well, there are different ways to go about finding it. One possibility is to look at triangle ABC and triangle ABC using the triangle sum theorem. The three angles have to add up to 180. So 25 plus 35 plus angle 2 has to add up to 180. So that's one way to get the fact that the measure of angle 1 is 120. Another way, if you want, another way is to look at angles 1 and 2 together. And they form a linear pair. Since angle 1 is equal to 60, I know angle 2 must equal 120 because linear pairs are supplementary. In other words, they form 180 degrees. Here's another example dealing with exterior angle theorem. We've got the exterior angle, 145, and it's remote interior angles. Again, those are the ones that don't touch the angle. The remote interiors are 95 and 2x. So the exterior angle theorem says the sum of the two remote interior angles, so 2x and 95, together they add up to 145. So if we subtract 95 from both sides, we see 2x is equal to 50, which means x in this case would be 25. So that means that this angle would be 2x or 2x25, so it would be 50 degrees. This last example, it's a good one. Take a second, you're going to want to write this down. Once again, sketch this out in your notes. We've got a bunch of different angles to find. It's like a little puzzle. So let's go piece by piece. First off, let's take a look at angle 1. Angle 1 is an exterior angle to this triangle, this one on the far left. Its remote interior angles are 80 and 60, and so that means angle 1 is the sum of the remote interior angles, or 140 degrees. Angle 2 forms a linear pair with angle 1, and so that means angle 2 must be equal to 40 degrees, since 40 plus 180 adds up to 180 degrees. Now to find angle 3. To find angle 3, we're going to use the exterior angle theorem once again. So take a look at this triangle. In this triangle, the red one, I see 105 is an exterior angle, and the remote interiors are 40 degrees and angle 3. So that means the sum of the two remote interior angles is equal to the exterior. And so we can solve, measure angle 3 is whatever 105 minus 40 is. So angle 3 is 65 degrees. Now to find, let's say we want to find angle 4 next, I see 4 and 105 degrees form another linear pair. So that means angle 4 must be 75 degrees. So I've got 75 is angle 4, angle 40 degrees. So in this last triangle, angle 5 is another exterior angle, and the exterior angle is the sum of the two remote interiors. So 40 and 75, together angle 5 should be 115 degrees.