Measure Theory by Donald Cohn | Amazon Link

[micromass]

• Author: Donald Cohn
• Title: Measure Theory
• Amazon Link: https://www.amazon.com/dp/0817630031/?tag=pfamazon01-20

 

[Category]

This is the book I used to learn measure theory. There is now a second edition featuring a slightly more friendly format, and a whole new chapter on probability.
I don't remember any lacking proofs with one exception - the approximation-by-simple-functions proposition. I guess this is because Cohn somewhat delays the introduction of the general definition of measurability. Rudin gives a concise (and unusually clear) proof in Real and Complex Analysis, Thm 1.17.

 

[PSarkar]

If you don't mind studying other things as well, you can try real analysis books by Rudin or Follands book: https://www.amazon.com/dp/0471317160/?tag=pfamazon01-20 .

 

[Axiomer]

This is also where I learned measure theory from (2nd edition). I found this text great for both learning and as a reference. I haven't used any other measure theory textbooks, but I didn't feel the need to with this book handy. There is a nice chapter on probability theory, and a proof of the Banach-Tarski paradox in the appendix.

 

[rezeew]

I am familiar with the concept of measure theory, which is a branch of mathematics that deals with the measurement of sets and their properties. I have read several books on this topic, and I must say that Donald Cohn's "Measure Theory" is a comprehensive and well-written guide to this subject.

The book covers all the important topics in measure theory, including measure spaces, sigma-algebras, Lebesgue measure, and integration. The author has a clear and concise writing style, making the material easy to understand for both beginners and experts in the field.

What I particularly appreciate about this book is the inclusion of numerous examples and exercises throughout the text, which help to reinforce the concepts and techniques discussed. The exercises also allow readers to test their understanding and apply the theory to real-world problems.

Moreover, Cohn's book goes beyond the traditional topics of measure theory and also delves into more advanced topics such as abstract measure spaces, product measures, and Radon-Nikodym theorem. This makes the book a valuable resource not only for students but also for researchers and professionals in the field.

Overall, I highly recommend "Measure Theory" by Donald Cohn to anyone interested in learning about this important branch of mathematics. It is a well-organized and comprehensive guide that provides a solid foundation for further study and research in measure theory. The Amazon link provided makes it easy to access and purchase the book, making it a convenient resource for anyone looking to expand their knowledge in this area.