Exercise books in analysis

Question

I'm studying Rudin's Principles of mathematical analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as a companion to Rudin.

The books I'm searching for should be:

• full of hard, non-obvious, non-common, and thought-provoking problems;
• rich of complete, step by step, rigorous, and enlightening solutions;

Answer 1

You can check these books:

http://www.amazon.com/Problems-Analysis-Second-Charalambos-Aliprantis/dp/0120502534/ref=sr_1_1?s=books&ie=UTF8&qid=1411894207&sr=1-1&keywords=problems+in+real+analysis

And

http://www.amazon.com/Problems-Real-Analysis-Advanced-Calculus/dp/0387773789/ref=sr_1_2?s=books&ie=UTF8&qid=1411894207&sr=1-2&keywords=problems+in+real+analysis

Answer 2

This is what I recommend to students learning analysis as a good companion:

http://minds.wisconsin.edu/handle/1793/67009

Answer 3

Check these books:

http://www.amazon.com/Problems-Variables-Lebesgue-Integration-Applications/dp/0070602212

http://www.amazon.com/Problems-Solutions-Undergraduate-Analysis-Mathematics/dp/0387982353/ref=sr_1_sc_1?s=books&ie=UTF8&qid=1411897062&sr=1-1-spell&keywords=Problems+and+Solutions+for+Undergraduate+Analysis+Rami+Shakarch

http://www.amazon.com/Problems-Theorems-Analysis--Integral-Einzeldarstellungen/dp/0387056726/ref=sr_1_2?s=books&ie=UTF8&qid=1411897112&sr=1-2&keywords=George+Polya+-+Problems+%26+Theorems+in+Analysis

http://www.amazon.com/Problems-Theorems-Analysis-Polynomials-Determinants/dp/3540636862/ref=sr_1_3?s=books&ie=UTF8&qid=1411897112&sr=1-3&keywords=George+Polya+-+Problems+%26+Theorems+in+Analysis

http://www.amazon.com/Problems-Mathematical-Analysis-Boris-Demidovich/dp/B0007BNL1W/ref=sr_1_1?s=books&ie=UTF8&qid=1411897098&sr=1-1&keywords=Demidovich+Problems+in+Mathematical+Analysis

They are available online.