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I'm looking for a big collection of exercises of functional analysis and measure theory. I know a lot of theory books which present some excercises (Brezis, Rudin, Lang, Royden, and others) but I was rather looking for something that would present much more exercises than theory and also report full solutions and detailed explanations.

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If you mean with measure theory also Lebesgue integration (measure and integration theory) and you want good exercises with solutions, i recommend amazon.com/Problems-Real-Analysis-Second-Edition/dp/0120502534 –  OBDA Mar 11 at 12:33
    
This looks great. Thanks. –  user73793 Mar 12 at 10:16

3 Answers 3

Introductory Functional Analysis and applications by Erwin Kreszig ?? By the way Brezis is very good in the sense the theory is kind of developed by asking you to do exercises.

For measure theory Halmos ?

But why don't you try this ? Prove all the propositions and theorems and corollaries by yourself without first looking at the explained text. That should be a good exercise.

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You can look at Real Analysis by Stein & Shakarchi. It has a lot of interesting as well as challenging exercises. The theory part is also quite nice. To me this book is the best.

The same author also has a book on Functional Analysis but it is probably a little advanced.

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Try the book Exercises in functional analysis by C. Costara and D. Popa: http://www.amazon.com/Exercises-Functional-Analysis-Mathematical-Sciences/dp/1402015607

Another excellent one is Theorems and problems in functional analysis by Kirillov and Gvishiani: http://www.amazon.com/Theorems-Problems-Functional-Analysis-Mathematics/dp/038790638X

Here is also a textbook with a huge amount of exercises, sometimes very original (and sometimes also quite hard): Elements of functional analysis by Hirsch and Lacombe; http://books.google.fr/books/about/Elements_of_Functional_Analysis.html?id=ahH_5yghkrEC&redir_esc=y

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The first two are probably the material I was looking for. Thanks. –  user73793 Mar 12 at 10:16
    
You're welcome! I hope you'll enjoy the reading. –  Etienne Mar 12 at 18:35

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