Measure Theory 21 | Outer measures - Part 2: Examples
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- Опубліковано 27 тра 2020
- Find more here: tbsom.de/s/mt
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: tbsom.de/s/community
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This is part 21 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here tbsom.de/s/start
These are the clearest videos on basic measure theory that I have seen on youtube. Your handwriting is very neat and I love the yellow background. It's a refreshing change from the black background that so many math teaching videos on youtube use.
If you have time, could you make some videos on measure theoretic probability? In particular, I am interested in conditional expectation from a rigorous measure theory point of view.
Thank you very much! Indeed I am working on videos about stochastics. However, they need a lot of time, sadly.
Have my Measure & Theory exam in a few days, would've been totally lost without these videos! Thank you :)
Thanks and you are welcome :)
Please, continue the series! Show a proof of Caratheodory’s theorem, at least. Your lectures are too good to be stopped at the most interesting point. :)
This series is simply brilliant, hats off to you
please talk more about lebesgue measurable functions, like littlewood's principles, egoroff's theorem, lusin's theorem. Thanks!
Thank you for this series, it’s very beautifully done, I enjoyed every minute of it!
fantastic lectures series. thanks making measure theory accessible.
Outstanding content, thank you so much for making these.
Sir please explain simple function and specially how to form sequence of simple functions of any general function...Also thank you because this channel is helpful for me
Looking forward to the next video. These videos are so good, it’ll be great to see the proof of Caratheodory.
Let no body dislike this video its too good doing ,no one is doing advance maths in this fashion thanks sir
I very much enjoyed the series so far. Topics are well structured & well explained. Many thanks. I would really appreciate videos on probability measures.
They will come :)
@@brightsideofmaths When? That would be great!
You are amazing thank you so much for this series. I can't thank you enough
You're so welcome! And thanks for the support!
Awesome video man :D
Thanx bruh!! For the video😊
In one of the last steps of the proof, you impose an order on the summation (you take the outer summation to be the n index and the inner summation to be the j index). Since both are infinite sums, doesn't this choice potentially affect the value of the summation and hence the validity of the proof? Thank you so much for these videos, they've been outstanding!
Good work! Always be careful when dealing with infinities. However, here we are dealing with non-negative numbers such that changing the order of the summation won't make a difference. Indeed, this is a special case of Fubini's theorem, see part 19.
This has been really helpful. Thank you so much. A quick question, why does the set A which is a subset of B, have more intervals than B?
Because A and B need not be partitioned the same way.
Please tell your name sir?
I loved this series, finally confident enough about measure theory now.
Thank you for providing such a content for free.
Love from india❤️❤️❤️
Thank you very much! All information are linked on my channel :)
This series is great. Is this the last one so far in the measure theory series?
At the moment, this is the last video in the series. I will continue it in the next month with a lot of nice stuff :)
@TomDaNub Of course! However, I have so many ideas and so little time.. I am not sure when I am finished here.
Thank you a lot for the videos. They are helping me a lot. Do you have any books you would recomend me to show the monotone convergence theorem for outer itegrals?
Thank you! I have to look if I find suitable books there.
Hi, thank you for the series very much and this is definitely the best measure theory course in youtube! However I do have a bit of doubt for this particular video. I feel like the last line in the video is incorrect? You can set the epsilon to be sufficiently small but it's still greater than 0. It's actually
Thank you very much! I don't exactly understand your problem. Maybe it helps you if you argue with the contraposition or by contradiction. Maybe assume a
@@brightsideofmaths Emmm, I will try to be clearer here. The result u had in the end is \phi(U A_n) 0. But I feel like even if you set \epsilon to be extremely small, you still can't draw the conclusion that \phi(U A_n)
@@joetrump1377 Set a = \phi(U A_n) and b = \sum \phi(A_n) and read my comment again :)
@@brightsideofmaths Oh, I c. That's because A_n s are fixed here and the I_{j,n}s and epsilons are the variants. Thx so much and hope to see more measure theory videos coming up if u r planning on that! Maybe on Liouville/Hausdorff measure?
Love you sir I wish you can do measurable function and go in depth I don't care how long it is I will like and subcribe and share to all my class mates
He has already covered measurable functions in-depth in this series.
Love from india
Sir why we take infimum?? In outer measure
To avoid double counting.