Measure Theory 21 | Outer measures - Part 2: Examples

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This is part 21 of 22 videos.

#MeasureTheory
#Analysis
#Integral
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I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[gamefaq]

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.

[AbhijeetVakil]

Have my Measure & Theory exam in a few days, would've been totally lost without these videos! Thank you :)

[elijahberegovsky]

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. :)

[StratosFair]

This series is simply brilliant, hats off to you

[elijahberegovsky]

Thank you for this series, it’s very beautifully done, I enjoyed every minute of it!

[uzomannaemekateflondon]

Let no body dislike this video its too good doing, no one is doing advance maths in this fashion thanks sir

[thesaddlepoint]

fantastic lectures series. thanks making measure theory accessible.

[johnstroughair]

Looking forward to the next video. These videos are so good, it’ll be great to see the proof of Caratheodory.

[yishi]

please talk more about lebesgue measurable functions, like littlewood's principles, egoroff's theorem, lusin's theorem. Thanks!

[yahyasaleh]

I very much enjoyed the series so far. Topics are well structured & well explained. Many thanks. I would really appreciate videos on probability measures.

[Stars]

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

[nada]

Outstanding content, thank you so much for making these.

[craigchikis]

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!

[tomasdougan]

You are amazing thank you so much for this series. I can't thank you enough

[debadattakar]

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❤️❤️❤️

[joetrump]

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 <= instead of < so you can't just remove the epsilon and preserve the inequality right? I think the overall idea is great but the proof needs to be a bit more rigorous? Pls correct me if I'm wrong.

[olapadezainab]

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?

[sueschrader]

This series is great. Is this the last one so far in the measure theory series?

[uzomannaemekateflondon]

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

[angelespinoza]

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?