# Suggestion on a book on Measure Theory

I want a book on Measure Theory extremely for self study .I want the book to have the following features:

• Topics explained in detail.I don't want a book that writes one line and asks the reader to check.
• Numerous solved examples which can help me to understand the topic.
• Good list of exercises (If hints are provided at the end then it's an added bonus).
• Please don't give the references as Rudin,Bartle etc. I have seen they don't have any solved examples ,only theory is explained followed by exercises.I get stuck while reading them.

Is it possible to have a book which contains the following features .I am really in need of it as I am studying on my own.

Are there any lecture notes /video lectures for the same .

• Sounds strange but describe in your question what you mean by "measure theory", there are just differend meanings of it (see tag list) , alternativly mention a book on the subject that you don't like – Willemien Feb 26 '16 at 15:05

## 7 Answers

Robert B. Ash's Probability & Measure Theory has complete solutions to many of the exercises.

Inder K. Rana's An Introduction to Measure and Integration is very nicely written with lots of exposition for those studying on their own.

Bruckner/Bruckner/Thomson's Real Analysis is full of motivational exposition and examples/problems, and it's freely available on the internet.

I found Measures, Integrals and Martingales by Rene Schilling to be quite a nice reading, with plenty of exercises and careful detailed proofs. To be fair, you will get stuck when reading books. This is usual and doesn't mean the book is not suited for you, or that it is (necessarily) poorly written. If a book is too soft you might end up learning too little to do anything. At any rate, give the above book a try, and also look at the classical references, and get stuck: self-studying means you will get stuck, and you will probably gain a lot from pushing through that situation than lowering the bar.

I really like Terry Tao's An Introduction to Measure Theory. I find his writing style very clear and I also like that the exercises are interspersed throughout the text, making it clear why they are useful and what is the relevance of the concepts presented in the text. Unfortunately, although it has solved examples, maybe they are not as much as you would like.

An older classic: Measure Theory, Paul Halmos, available (legitimately) here. Perhaps not what you're after, though: the examples are the exercises :)

Have you seen Royden's book? It's less definition/theorem/proof/ than Halmos, but still perhaps not enough so for what you seek.

The book used at the University of Copenhagen is Ernst Hansens Measure Theory. It is an excellent book that continues from general measure theory into probability theory.

I personally quite like Fremlin's books. part 1 is here, and all $\TeX$ sources can be found here, as well as info on how to order physical copies. He has a quirky style but lots of examples and exercises (not worked, normally). It's huge, but good for self-study. Part 1 will give you a taste (and is the smallest one).

Try the book by [Halsey_Royden,_Patrick_Fitzpatrick]_Real_Analysis

It is extremely well written with lots of exercises to solve . The exercises start from a very elementary level and then slowly but steadily become rigorous.

Another book is [Richard_Wheeden_Antoni_Zygmund]_Measure_and_Integration.

It is also on the same line as above but includes more exercises than the above.

The books start with Lebesgue Measure on $\Bbb R$ and then move onto the Abstract Measure Space making them suitable for self-study.

Also most of the solutions are available online and also on MSE.