Principles of Real Analysis

Rating:
Summary: One of the best
Review: An ideal text for a first-year graduate students in mathematics studying Real Analysis. The exposition is complete and very clear, including a lot of optional material for the curious. A detailed introduction to Functional Analysis is also included. Those needing the infamous Radon-Nikodym theorem and theory of signed measures will need to skip around since this is presented in the very last chapter (not a big problem). Also, consult the authors' companion text Problems in Real Analysis, which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, a highly recommend text.

Rating:
Summary: Very Mediocre Contents, Terrible Aesthetics
Review: I was very disappointed in this book and judging from the steady decline of the resale price here on amazon.com, I can see others agree.

First of all the book looks like it was photocopied in someone's basement - the text is completely faded out and paper feels terrible. For almost $100, I expect a little more.

The actual contents of the book are not much better. I found Royden (the required text for our class) to be very sparse and was hoping for something to fill in the details. This book did little to help. It covers integration in a rather idiosyncratic way, devotes little time to differentiation, and says nothing about convexity.

If you are looking for a good anaysis book I recommend either "Lebesgue Integration on Euclidean Space" by Frank Jones or the slightly more abstract "Real and Functional Analysis" by Serge Lange