Customer Reviews

An Introduction to Measure and Integration (Graduate Studies in Mathematics)

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This is an amazing book; its clarity is outstanding throughout. However, I want to voice serious reservations about it due to an abundance of errors; I am reviewing the second edition published by the AMS.

This book has more errors than any other math book I have read. These errors include minor typographical errors like sloppy spacing, to equations with the terms included in the wrong order or on wrong lines, misnumbered references to earlier results, and occasional abuse of notation that hinders mathematical rigour. There are substantive errors as well, including the citing of a source for a proof of a theorem that is not actually proved in the cited source.

Errors aside, this is one of the clearest and best motivated expositions of measure theory I have been able to find. The book moves slowly, but never too slowly; it explores essential questions that a student should consider, like counterexamples, converses, and the subtle distinctions between different strengths of conditions. I find this thoroughness very welcome; most texts in measure theory present the most logically direct path to a bare-bones collection of useful results, an approach that doesn't necessarily help students.

The first chapter, on Riemann integration, is unique. The topic is explored in much more depth than in most analysis texts. Most students feel they understand Riemann integration; this book will likely convince them that they do not--and then it will fill the gaps in their understanding. The counterexamples in this book are outstanding--simple, worked through with clarity, and deep.

I think this book would make an outstanding textbook on measure theory, and it is one of the few texts that is good for self-study. I just wish the errors could be corrected; I would then rate it 5 stars without a doubt.