Riemann integral vs. Lebesgue integral [dark version]

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Here, I explain the differences between the Riemann integral and the Lebesgue integral in a demonstrative way.

I hope that this helps students, pupils and others.

Spanish subtitles by Jorge Ibáñez. Thank you :)

#MeasureTheory

0:00 Introduction
0:30 Riemann integral
2:00 Problems of Riemann integral
7:50 Riemann integral definition
9:13 Lebesgue integral - idea

 (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)

[surendrabarsode]

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

[jukkejukke]

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

[homosapien]

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

[mastershooter]

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

[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?

[dr.hanyeldeeb]

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

[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.

[DanielSilva-gcxz]

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

[colinjohnson]

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

[DrMcCrady]

Do you have any advice about growing your YouTube channel?

[meteor]

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