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 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 tomeasure@axler.net).
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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)
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