Measure, Integration & Real Analysis

Graduate Texts in Mathematics #282

by Sheldon Axler

About the Author.- Preface for Students.- Preface for Instructors.- Acknowledgments.- 1. Riemann Integration.- 2. Measures.- 3. Integration.- 4. Differentiation.- 5. Product Measures.- 6. Banach Spaces.- 7. L^p Spaces.- 8. Hilbert Spaces.- 9. Real and Complex Measures.- 10. Linear Maps on Hilbert Spaces.- 11. Fourier Analysis.- 12. Probability Measures.- Photo Credits.- Bibliography.- Notation Index.- Index.- Notes on Typesetting.

Genres: Mathematics, Textbooks, Science, Amazon

432 pages, Paperback

Published December 4, 2019

Reviews

[Mark Moon · Rating 5 out of 5]

This is a great intermediate analysis book: perfect for someone who's had an introduction to real analysis (see the Supplement on Axler's site, where a pdf of the book is also available for free, for the introductory real analysis you should know going in) and wants to be very prepared for a more advanced analysis course (like Stein & Shakarchi's "Princeton Lectures in Analysis" or Reed & Simon's "Methods of Modern Mathematical Physics").

As always with Axler, the exposition is very clear, and there are many illuminating examples and exercises. The last chapter, on probability, provides an excellent "dictionary" between probability-theoretic terminology and the measure-theoretic terminology used in the rest of the book, and I found this especially useful.

[Kent Sibilev · Rating 5 out of 5]

I am a big fan of 'Linear Algebra Done Right' by the same author. This book is more advanced theory of real analysis of twentieth century: Measure theory, Banach and Hilbert spaces, etc with applications to the Fourier Analysis and Probability Theory. This is such a wonderful and concise exposition of these ideas with a very decent problems set for self studying. Also kudos to the author for making this book public.

[Jens Lang Rasmussen · Rating 5 out of 5]

Read the first six chapters. The book is clear and pedagogical and succinct at the same time, so it is both a good intro and later reference. I need a break with something more practical before tackling the rest of the book.

[Owen Levens · Rating 5 out of 5]

Call me an LP space the way I’d let this book Lick my Pussy

[Adam · Rating 4 out of 5]

I think this book is excellent for what it does: Speak in a familiar language, and at a comfortable pace, to a graduate mathematics student. That is to say, the audience must already be quite mathematically mature -- but if they are, then they will get a lot out of this textbook, with less struggle than they would from other textbooks on similar topics.

That said, I'm not sure I would recommend this as a teach-yourself kind of textbook. I think this text would require, for most readers with an undergraduate background, an instructor to explain and smooth over some of the presentation.