Measure, Integration & Real Analysis

Sheldon Axler is Professor of Mathematics at San Francisco State University. He has won teaching awards at MIT and Michigan State University. His career achievements include the Mathematical Association of America’s Lester R. Ford Award for expository writing, election as Fellow of the American Mathematical Society, over a decade as Dean of the College of Science & Engineering at San Francisco State University, member of the Council of the American Mathematical Society, member of the Board of Trustees of the Mathematical Sciences Research Institute, and Editor-in-Chief of the Mathematical Intelligencer. His previous publications include the widely used textbook Linear Algebra Done Right.

“This textbook is addressed to students with a good background in undergraduate real analysis. Students are encouraged to actively study the theory by working on the exercises that are found at the end of each section. Definitions and theorems are printed in yellow and blue boxes, respectively, giving a clear visual aid of the content.” (Marta Tyran-Kamińska, Mathematical Reviews, May, 2021)“The book will become an invaluable reference for graduate students and instructors. Those interested in measure theory and real analysis will find the monograph very useful since the book emphasizes getting the students to work with the main ideas rather than on proving all possible results and it contains a rather interesting selection of topics which makes the book a nice presentation for students and instructors as well.” (Oscar Blasco, zbMATH 1435.28001, 2020)

• 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.- Colophon: Notes on Typesetting.