Measure Theory - 1: Geometric and Intuitive Ideas -1

The first three in this series try to give some intuitive and geometric ideas underlying the theory Lebesgue measure. Viewers who are too formal and who believe that any statement in mathematics should be rigorous are requested to skip these three videos! Like any new idea, measure theory also starts with vague questions, still more vague answers and as one goes along one makes them more precise.. I try to exhibit the agonizing thought process (not necessarily of the creator of the theory, Lebesgue) as I went through this while learning and then teaching to my classmates and students later.

Do not aim for 100% understanding. Try to get the ideas and think over them. My students who did this actually claimed that measure theory was an easy one! Can you believe this? Give it a try.

I dedicate this series to Professor Bhaba Sarma, IITG who has been editing all my 350+ videos. Without his enthusiastic help and conviction that this channel will help students of Mathematics, I could not have gone this far.

I also thank the members of the MTTS Trust who share Bhaba's conviction and lent their support for this channel in various form such as recommending it to their students and audience of their lectures.

Finally, I thank those who persuaded me to start the series on Measure theory. Hope they like these videos.

Timestamp:
00:00 Introduction
0:54 Aim of the lecture
2:05 About email and list of videos
4:22 What does measure theory mean?
7:18 Review of Riemann integration
20:11 Riemann integration in terms of step function
21:50 Difference b/w R.D and lebesgue
27:02 Some advice
30:35 Difficulty in defining measure in Dirichlet's function
35:18 Measure in n-dim subsets
57:24 What we did and will do in upcoming videos
58:35 Outro

Music I use: Bensound
License code: BGVUHKIWPLP92UKG

[joyitabanerjeeganguly]

What an introduction sir. I can completely visualize all three notions of measure after watching this.

[MathematicalDimension]

Sir please try to deliver deeper view as much as can be possible because measure theory is subject for which i am waiting eagerly. Thank you sir.

[uttiyapaul]

The best introduction to measure theory I have seen so far....take a bow sir

[iamppk]

This video Asks many why's and how's and Answers them informally and intuitively with lots of analogies... I feel that this is a perfect introduction to the subject sir... now we have a motivation to learn measure... Understoood and enjoyed.... Thank you so much sirr...

[ankitaKumari]

Thoroughly enjoyed every bit of it. Thank you sir :)

[rumipal]

Thank you sir for helping us to get the intutive ideas of this which is abstract to me.

[abhameenakshi]

Please upload further sessions as well

[mrrajpurohith]

Rajinikanth in acting : :kumaresan sir in teaching.

[iamppk]

19:42 Sir, I think, the integral of f = LUB{integral of s: 0<= s <= f on [a, b]} where s stands for step functions, and is not same as LUB{s: 0<= s <= f on [a, b]}...

[tanmaymath]

Sir i request you to not be limited only to Lebesgue measure space but also please link Lebesgue measure theory to abstract measure theory also..for general perspective .