Integration of measurable functions - Lec06 - Frederic Schuller

[@atakankasloglu]

The best lecture video i've seen since Walter Lewin. Congratulations and thanks.

[@Afxonidis]

That was maybe the best explanation I have ever heard of the quotient space. Brilliant work!

[@shuaiwang5606]

I tried to self study and different videos, your explanation is sooo clear and easy to understand, wish I could attend your class!!!!!

[@lordeuler2912]

Hölders and Cauchys inequality should both be multiplications and not additions.

[@antoniolewis1016]

yes

[@benpovar3914]

The prof. meant Minkowski inequality

[@alexgoldhaber1786]

The important thing now is that I learned how to pronounce ö as in Hölder!

[@connorfrankston5548]

@@benpovar3914 no, he must have made a mistake. The Cauchy-Schwarz inequality is definitely with multiplication, and the Hölder inequality too.

[@adambruce1688]

@@benpovar3914 Minkowski is slightly different. ||f+g||

[@jean-pierrecoffe6666]

Such a great lecture. Absolute clarity in all of the explanations

[@mathjitsuteacher]

It is important to notice that the pointwise supremum of nonnegative measurable functions is also a nonnegative measurable function and this allows you to integrate it.

[@timelsen2236]

Greatest mathphysics on line, and loved the student interaction.

[@RudranarayanPadhy-x6g]

Wonderful teachig style with sufficient content covered less than 2 hours. Thank you sir.

[@jwp4016]

35:06 the measure of the pre image of z? Shouldn't it be the measure of the pre image of [z, infinity) ? Anyway, he is easily the best math teacher I've ever seen in my math learning journey.

[@jwp4016]

I missed 1:13:36

[@joaodfbravo]

@@jwp4016 Why is it not just preim(z)?

[@sardanapale2302]

Yes ... in the sketch he did preim(z) has zero measure

[@sardanapale2302]

@@jwp4016 Its still false, on preim[0,z) f will be < z... you need preim[z,oo) so that on that set f >= z and you will get a lower bound of the integral of f...

[@sardanapale2302]

lol he finally corrects that afterwards :P

[@AmatisoveLove]

This really is a great video, I'll definitely watch more of your lectures! Helped me a lot, thanks.

[@circuithead94]

The clarity of Schuller's explanation is amazing.

[@stefanogioberti]

Such a clear lecturer. Makes the difficult easy. Many thanks.

[@tim-701cca]

Very clear. The set of your mistakes has measure zero.

[@tim-701cca]

At 1:09:43, (ii) lim \int |fn-f| = 0 , not only finite. (corrected) At 1:11:11 it can be R bar, with infinity since f,g are integrable, and therefore \int f is finite by definition.

[@user-bk2fo7ny9s]

this is elite level teaching ...

[@ΣτέργιοςΚατσογιάννης]

1:20:50 Progress to the direction of Hilbert and Banach spaces... and why this matters when one does solid state physics!

[@sisayketema3415]

Dear Dr. i glads to follow such interesting lecture ...really really it was nice lecture. before this lecture i am not familiar with this concept after following your lecture things was clear for me thank you very much.keep it up

[@michielsnoeken5596]

Why is the singleton {s_i} measurable, since a singleton in the standard topology is not open and therefore also not an element of the sigma-algebra?

[@HilbertXVI]

But the borel algebra contains a lot more than just open sets. You could write {s_i} as a countable intersection of the sets (s_i - 1/n, s_i + 1/n), each of which is open, and hence measurable. So the intersection {s_i} is also measurable.

[@MrLikon7]

there is an easier way to see this: the complement of a singleton is open in the standard topology. but the sigma-algebra is closed under complement-taking, so the singleton is in it. in fact, the borel sigma-algebra contains all the open AND closed sets, furthermore all the half-open intervals and so on

[@millerfour2071]

25:03, 42:35, 1:12:28 (35:58), 1:25:17, 1:32:00, 1:35:10, 1:38:38, 1:44:03, 1:48:48

[@abdellatifelgrou7772]

Just a remark teacher chaucy inequality with product not a sum : ||

[@jacoboribilik3253]

Great lecture. Much appreciated.

[@Anthony-db7ou]

I was the one who could be easily mislead by this. I haven’t taken measure theory formally, but need to learn more for my upcoming program in finance! You’re series is definitely unambiguously presenting the math, and I won’t say that about anything else I’ve come across. Any book recommendations?

[@benwincelberg9684]

Real Analysis by Royden

[@lugia8888]

Needs more examples

[@mastershooter64]

"A User-Friendly Introduction to Lebesgue Measure and Integration" by Gail S. Nelson, it is a really nice and friendly introduction to measure theory. Has lots of intuitive explanations and includes illustrations, all the while being completely rigorous.

[@allwanamar1]

this is an excellent lecture sir.

[@Ciupakabrinas]

Thanks for the lecture! You make Lebesgue integration seem easy.:)

[@wenzhang365]

Amazing lectures. Is there a textbook(s) for this course?

[@jiahao2709]

why these lectures, youtube don't have automatical translation?

[@peterpalumbo3644]

Are there any problem sheets for people viewing these lectures on You-Tube, are the Experimental lectures on You-Tube?

[@fredxu9826]

QM lectures turn out to be great for anyone interested to start functional analysis

[@paulserna2104]

It is clear and tidy.

[@lisaking3996]

I like his wavy norm sign

[@farshadnoravesh]

a great lecture

[@juliogodel]

Excellent lecture, Thanks.

[@kevinmc7993]

Very understandable

[@ryanchiang9587]

i remember these terminologies such as borel sets, sigma-algebras...etc.

[@minexe]

thanks

[@وسنحسينعلي-غ6ظ]

Please doctor, l need to solve this equations. : 1: show that the step function f (X) =[x] is measurable function on [1,3] And 2: if f is measurable function over a measurable set E then f is measurable over any measurable subset A of E

[@ChaimaChaima-gb4ng]

Good🤓

[@dr-rer-nat-jonathan]

height times width (not with :D)

[@maciej12345678]

very fine but where are proof of theorems

[@gooomaaal]

good joke 1:11:48

[@ciruzzobello3108]

1:05 point aus... Oops, wrong language :-)

[@atzenkack]

cocaine? :D

[@hassaannaeem4374]

the gender jabs never get old