Riemann integral vs. Lebesgue integral [dark version]

[@surendrabarsode8959]

Indeed the best explanation I have come across so far on this topic!! Precise, clear and easily understandable by anyone!! Perhaps, you could add a few examples where the integrals are calculated under both the methods and where only Lebesgue integral is calculated for some higher dimensional domain. Thanks and regards

[@jukkejukke5386]

Danke Julian. Bestes Video zum Thema auf KZbin was das Big Picture erklärt. Das mit dem Höherdimensionalen wird nie am Anfang erklärt sondern die zu abstrakte rational-reelle 0, 1 Funktion.

[@homosapien5684]

Okay this is spooky. Just when i am having trouble with a topic, you release a video of it.

[@mastershooter64]

I feel like you can write a python script that automatically takes all the videos, makes their background black then uploads them to youtube :)

[@brightsideofmaths]

Indeed!

[@scollyer.tuition]

Very nice overview. Although a measure is defined on a sigma algebra, am I right in thinking that the pre-images on the x-axis generated by an arbitrary partition of the y-axis cannot, in fact, produce a sigma algebra? It seems that in this case at least we could construct the theory using a smaller structure than a sigma algebra - or am I confused here?

[@brightsideofmaths]

You could work with less structure in some contexts. However, you can watch my measure theory videos to see why sigma algebras are so useful here.

[@DanielSilva-gc4xz]

If you're posting bright and dark versions of the same video then you could have a channel called "The Dark Side of Mathematics" lol

[@brightsideofmaths]

Yes :D

[@yongmrchen]

Can I say that Lebesgue integral is a generalization of Riemann integral and the latter is a special case of the former? The reason that we don’t need measure theory for Riemann is because the partition of X is a valid measure by itself.

[@brightsideofmaths]

The Lebesgue integral is different than the Riemann integral but the Lebesgue integral covers all Riemann integrable functions and gives the same value to them.

[@yongmrchen]

@@brightsideofmaths Thank you for the explanation 🙏

[@brightsideofmaths]

@@yongmrchen Thanks for your support!

[@colinjohnson8044]

Your example around 9:00, is that not just the Darboux Integral? Love the dark formats btw :)

[@yodas6798]

amazing video, helped me so much!

[@brightsideofmaths]

Nice :) I am really glad about that!

[@Profejuanca]

Amazing

[@meteor8076]

So in order to work with Lebesgue integral we need to know measure theory ??

[@brightsideofmaths]

Yes :)

[@dr.hanyeldeeb4259]

I want to obtain pdf lectures of KZbin videos on measure theory and complex analysis is it possible to send it to me?

[@brightsideofmaths]

Yes, you can get them as a Steady supporter! tbsom.de/s/subscribe

[@antoine5571]

Great video thank you

[@brightsideofmaths]

Glad it was helpful!

[@DrMcCrady]

Do you have any advice about growing your KZbin channel?

[@brightsideofmaths]

No, not really :D

[@VandalIO]

which one is better ?

[@brightsideofmaths]

Lebesgue :D

[@leesweets4110]

What is your accent?

[@brightsideofmaths]

German