Is Donald Cohn's second edition of Measure Theory good?

Question

I read (most of) Baby Rudin, and now i am interested in learning more stuff about real analysis, in particular measure theory and functional analysis. Is "Measure Theory: Second Edition" by Donald L. Cohn a good introduction book in these subjects? (good = comprehensive, has a lot of medium/hard practice problems and more importantly, counterexamples). If not, are there any companion books/notes i can use while reading it?

Answer 1

I think it's quite a good book, you can also use it as a reference book later on. He does some strange stuff like his definition of $L^\infty$ and also doesn't just assume $\sigma$-finiteness, and some of his proofs are a bit long (like the proof of change of variables is 11 pages long or something). But it is a beautiful book, he doesn't leave out proofs as an exercise if you prefer that although some exercises do provide alternative proofs or such. The last few chapters are also optional, mostly if you're interested in the subject matter like probability theory, Polish spaces and more. The appendices are also quite comprehensive.

Edit: He does also provide some counterexamples, for example the Banach-Tarski paradox, the Cantor set and function and Vitali sets.