Yes, I know that this question has been asked before, but let me explain why I am asking again.
I have had the experience of taking a measure theory course using the book by Donald Cohn on the subject, and the exercises were tough.
Let me explain some features of a measure theory book I would be interested in:
- exercises of various levels of difficulty (if possible, in sorted order or marked to indicate difficulty level)
- a solutions manual to (at least some of) these exercises
- would like the book to explain some of the tricks used in harder analysis problems
- would like the book to have good exposition that helps to build intuition
- would like the book to have most of the standard material on measure theory required for graduate mathematics
I don't claim that these criteria are anything more than vague, but I hope that they give a sense of what I'm looking for. For example, I liked Aluffi's Algebra book, because it has many of these feature with out sacrificing too much rigor/material needed in a graduate textbook. If possible, it'd be great for this book to cover the needed material on measure theory required for graduate mathematics. I mention Probability Theory in the title as well, on the off chance that you happen to know of a book that does these things for Probability Theory.
