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Graduate Texts in Mathematics
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Open Access This content is freely available online to anyone, anywhere at any time.

Measure, Integration & Real Analysis

Authors: Axler, Sheldon

  • Electronic version is free to the world via Springer’s Open Access program
  • Provides student-friendly explanations with ample examples and exercises throughout
  • Includes chapters on Hilbert space operators, Fourier analysis, and probability measures
  • Prepares students for further graduate studies by promoting a deep understanding of key concepts
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eBook  
  • ISBN 978-3-030-33143-6
  • The ebook is not yet available online.
Hardcover 49,99 €
price for Korea, Republic of (South Korea) (gross)
  • 까지: January 2, 2020
  • ISBN 978-3-030-33142-9
  • Free shipping for individuals worldwide
About this Textbook

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.

Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.

Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.

Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.

About the authors

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.

Buy this book

eBook  
  • ISBN 978-3-030-33143-6
  • The ebook is not yet available online.
Hardcover 49,99 €
price for Korea, Republic of (South Korea) (gross)
  • 까지: January 2, 2020
  • ISBN 978-3-030-33142-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Measure, Integration & Real Analysis
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
282
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Sheldon Axler
eBook ISBN
978-3-030-33143-6
DOI
10.1007/978-3-030-33143-6
Hardcover ISBN
978-3-030-33142-9
Series ISSN
0072-5285
Edition Number
1
Number of Pages
X, 435
Number of Illustrations
21 b/w illustrations, 20 illustrations in colour
Topics