A more advanced book on real analysis

Question

I have already studied "Advanced Calculus Second Edition by Patrick M. Fitzpatrick" on real analysis. It is the best book on real analysis I found that can be studied by self-learning with high-school math knowledge, even better than Rudin's analysis. It is best because it is 1- rigorous but still simple, 2- comprehensive (beautifully 590 pages!), 3- VERY readable for self-learning (most important reason).

I want to start the next book on real analysis, i.e., MORE ADVANCED. But I need it to have all the three mentioned criteria. I would appreciate it if someone helps me. Thanks a lot.

Answer 1

The 3 major books for beginner graduate level real analysis are:

1) Royden & Fitzpatrick, Real Analysis

2) Folland, Real Analysis

3) Rudin, Real & Complex Analysis.

A good book for the transitionary level is N. L. Carothers' Real Analysis.

I prefer (2) and (1) in combination for exposition (esp. for Radon-Nikodym, (1) is clearer than (2)), but (3) has the best problems. Carothers is a nice book to have on hand, thoguh.