Real Analysis: Theory Of Measure And Integration

by J. Yeh

This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.

Genres: Mathematics

760 pages, Paperback

First published June 28, 2006

Reviews

[Tony · Rating 5 out of 5]

Possibly THE best introduction to measure theory and integration one could get. I have tried Measures, Integrals and Martingales by Schilling and this, and I would have to say this is much better.

This book is very comprehensive and detailed, which is of course necessary for an introductory text. Schilling's text fails at this. As a consequence, this is a very didactic book which is amazing for those self studying it for the first time!

Both texts are introductory, and both require, as a prerequisite, a rigorous course in advanced calculus (sequences, series, concept of continuity, pointwise/uniform convergence, etc). Both also come with exercises (with solutions in a separate text).

To summarize: if you really want to understand the material, I suggest you go with this book. Otherwise, if you want a concise book that is introductory, go with Schilling's text.

10/10 for Yeh, 2/10 for Schilling.