The Best Book on Measure Theory

In this video, I'm discussing my favorite book on measure theory, and why I think it is the best book to learn this subject from. The book is an essential resource for graduate students in mathematics, and for anyone looking to have a better understanding of analysis in mathematics.

[Ayu]

I've worked through many measure theory books, including this one, and Rene Schilling.

I think the Tao book is good, but not the best one for a good, gentle, intuitive start that ramps up to more abstract theory. I would recommend "Measure, Integral and Probability" by Kopp and Capinski.

This book is so great. It has diagrams, intuitive explanations and easy cases explained in detail before giving you the full abstract theorem. Every theorem is given a proof, either immediately or at the end of the chapter if you want to try it yourself. Every exercise has a solution - absolutely invaluable for a first time learner. I wish every Mathematics textbook aimed at undergraduates was like this.

[lukeatlas]

I appreciate your videos, don't let the negative comments stop you! Your responses to them speaks highly of your character positively!

[active]

From a didactical point of view, I highly recommend: René Schilling, "Measures, Integrals and Martingales" (2nd edition), Cambridge University Press.

[javiermd]

I also strongly recommend his analysis books.

[爸爸到底-sx]

The online notes version of this book is far superior than other forms since you also get many discussions in the comment section that extend the original material.

[TranquilSeaOfMath]

I may have used this or something similar. It was helpful to get Tao's perspective after seeing another Messure Theory text.

[davidberkowitz]

Most books have typos but I find it funny you happened to pick a page with one. Pause at 0:27.

[ElectricalReview]

*I read measure theory from book by C.D Aliprantis*

[IsomerSoma]

The best measure theory book i know is by elstrod. I am afraid there only exists a german version, but it is beautifully written. It is high-level for an introductory text on the subject. Thr unique thing about it is that it while introducing a new concept opens up with the historic problem and outline of the development that lead to the modern theory first. It also has some mini biographies of the mathematicians introduced through their theorems (like 1 page). This and its beautiful language in general (it has very tight proofs) makes it a joy to read. It is also very complete making it great for reference. So it fulfills 3 roles: reference material, great to read and a material to learn from with very challenging exercises.

[phosphor]

could you possibly do one for numerical analysis? i dont think there are many youtube videos on numerical analysis books

[kobemop]

I come from a physics background. I have a bias towards Barry Simon's and Michael Reed's series on analysis (but geared towards mathematical physics).

[loganm]

I quite liked Bartle's book for a very brief look at MT.

[malaygarg]

What do you suggest are the prerequisites to this ?

[MonjeMonoIA]

Great, was searching for a book on measure theory and Tao is always a guarantee

[ege]

i hate myself for being incredibly worthless compared to tao. if he can exist, why should i?

[jalepezo]

As stats major, I am jealous XD I love proofs

[navjot]

Sheldon Axler has an even better book now, and it's free 😁

[marciamarquene]

DI o nome da pessoa da minha vida é o nome dele é o nome dele é v o número da sua

[axe-vwek]

Dude just assumed tao book was better than other texts because of his name lol. You clearly don't know any higher level mathematics and I bet you barely actually went through the book. Both folland and rudin texts cover most of what tao's book covers lol. Also tao does not cover Bochner integration or radon integration/measures. I can tell your mathematics knowledge is quite weak since you're referring to "strong intuition" lol.

[marinchan]

What about Rudin and Royden? Those are masterpeices.