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
Danke Julian. Bestes Video zum Thema auf TH-cam was das Big Picture erklärt. Das mit dem Höherdimensionalen wird nie am Anfang erklärt sondern die zu abstrakte rational-reelle 0, 1 Funktion.
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?
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.
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.
![Measure Theory 13 | Lebesgue-Stieltjes Measures [dark version]](http://i.ytimg.com/vi/N_x-JrU3C_Y/mqdefault.jpg)
![Measure Theory 13 | Lebesgue-Stieltjes Measures [dark version]](/img/tr.png)
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
Danke Julian. Bestes Video zum Thema auf TH-cam was das Big Picture erklärt. Das mit dem Höherdimensionalen wird nie am Anfang erklärt sondern die zu abstrakte rational-reelle 0, 1 Funktion.
Okay this is spooky. Just when i am having trouble with a topic, you release a video of it.
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
Yes :D
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?
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.
I feel like you can write a python script that automatically takes all the videos, makes their background black then uploads them to youtube :)
Indeed!
I want to obtain pdf lectures of TH-cam videos on measure theory and complex analysis is it possible to send it to me?
Yes, you can get them as a Steady supporter! tbsom.de/s/subscribe
Do you have any advice about growing your TH-cam channel?
No, not really :D
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.
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.
@@brightsideofmaths Thank you for the explanation 🙏
@@yongmrchen Thanks for your support!
amazing video, helped me so much!
Nice :) I am really glad about that!
Your example around 9:00, is that not just the Darboux Integral? Love the dark formats btw :)
So in order to work with Lebesgue integral we need to know measure theory ??
Yes :)
Amazing
Great video thank you
Glad it was helpful!
which one is better ?
Lebesgue :D
What is your accent?
German