Measure, Integration & Real Analysis

Sheldon Axler

This book seeks to provide students with a deep understanding of the definitions, examples, theorems, and proofs related to measure, integration, and real analysis. The content and level of this book fit well with the first-year graduate course on these topics at most American universities. This textbook features a reader-friendly style and format that will appeal to today's students.


Measure, Integration & Real Analysis was published in Springer's Graduate Texts in Mathematics series in 2020. The book was published with a Creative Commons Attribution-NonCommercial license. Thus the electronic version of the book is available without cost by clicking below.

The review of undergraduate real analysis freely available at the following link was written by the author of Measure, Integration & Real Analysis to help students review prerequisite material.

The print version of Measure, Integration & Real Analysis is available from Springer, Amazon, and Barnes&Noble.

Corrections and suggestions for improvements are truly appreciated (send them to measure@axler.net).
Follow AxlerLinear on Twitter Follow @AxlerLinear on Twitter for updates on Measure, Integration & Real Analysis.

Excerpts from zbMATH review of Measure, Integration & Real Analysis

The book is a perfect introduction to graduate students into the theory of measure and Lebesgue integration together with some topics in Real Analysis. ... The presentation is a gentle approach to serious mathematics with many examples and detailed proofs. ... The book will become an invaluable reference for graduate students and instructors.
(full review in zbMATH)


Excerpts from reviews of the author's book Linear Algebra Done Right

Altogether, the text is a didactic masterpiece.
zbMATH

Axler demotes determinants (usually quite a central technique in the finite dimensional setting, though marginal in infinite dimensions) to a minor role. To so consistently do without determinants constitutes a tour de force in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose... The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library.
Choice

The determinant-free proofs are elegant and intuitive.
American Mathematical Monthly

Clarity through examples is emphasized... the text is ideal for class exercises... I congratulate the author and the publisher for a well-produced textbook on linear algebra.
Mathematical Reviews


Sheldon Axler's publications
Sheldon Axler's home page