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Measure, Integration & Real Analysis

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Sheldon Axler, San Francisco State University

Copyright Year: 2020

Last Update: 2021

Publisher: Sheldon Axler

Language: English

Formats Available

Conditions of Use

Attribution-NonCommercial Attribution-NonCommercial

Table of Contents

  • 1 Riemann Integration
  • 2 Measures
  • 3 Integration
  • 4 Differentiation
  • 5 Product Measures
  • 6 Banach Spaces
  • 7 Lp Spaces 
  • 8 Hilbert Spaces
  • 9 Real and Complex Measures
  • 10 Linear Maps on Hilbert Spaces
  • 11 Fourier Analysis
  • 12 Probability Measures 

Ancillary Material

About the Book

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.

About the Contributors


Sheldon Axler was valedictorian of his high school in Miami, Florida. He received his AB from Princeton University with highest honors, followed by a PhD in Mathematics from the University of California at Berkeley. As a postdoctoral Moore Instructor at MIT, Axler received a university-wide teaching award. He was then an assistant professor, associate professor, and professor at Michigan State University, where he received the first J. Sutherland Frame Teaching Award and the Distinguished Faculty Award.

Axler received the Lester R. Ford Award for expository writing from the Mathematical Association of America in 1996. In addition to publishing numerous research papers, he is the author of six mathematics textbooks, ranging from freshman to graduate level. His book Linear Algebra Done Right has been adopted as a textbook at over 300 universities and colleges.

Axler has served as Editor-in-Chief of the Mathematical Intelligencer and Associate Editor of the American Mathematical Monthly. He has been a member of the Council of the American Mathematical Society and a member of the Board of Trustees of the Mathematical Sciences Research Institute. He has also served on the editorial board of Springer’s series Undergraduate Texts in Mathematics, Graduate Texts in Mathematics, Universitext, and Springer Monographs in Mathematics. 

He has been honored by appointments as a Fellow of the American Mathematical Society and as a Senior Fellow of the California Council on Science and Technology. Axler joined San Francisco State University as Chair of the Mathematics Department in 1997. In 2002, he became Dean of the College of Science & Engineering at San Francisco State University. After serving as Dean for thirteen years, he returned to a regular faculty appointment as a professor in the Mathematics Department.