© 2017

Modern Real Analysis


Part of the Graduate Texts in Mathematics book series (GTM, volume 278)

Table of contents

  1. Front Matter
    Pages i-xi
  2. William P. Ziemer
    Pages 1-10
  3. William P. Ziemer
    Pages 11-32
  4. William P. Ziemer
    Pages 33-67
  5. William P. Ziemer
    Pages 69-118
  6. William P. Ziemer
    Pages 119-139
  7. William P. Ziemer
    Pages 141-208
  8. William P. Ziemer
    Pages 209-258
  9. William P. Ziemer
    Pages 259-300
  10. William P. Ziemer
    Pages 301-316
  11. William P. Ziemer
    Pages 317-333
  12. William P. Ziemer
    Pages 335-374
  13. Back Matter
    Pages 375-382

About this book


This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations.

This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.




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Authors and affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

About the authors

William P. Ziemer is Professor Emeritus of Mathematics at Indiana University, and is the author of the highly influential GTM (vol. 120), Weakly Differentiable Functions.

Monica Torres is Associate Professor of Mathematics at Purdue University, specializing in geometric measure theory and partial differential equations.

Bibliographic information


“This book provides an accessible self-contained introduction to modern real analysis suitable for graduate students with an understanding of advanced calculus. It may also provide a useful reference for more experienced mathematicians. The focus of the book is on measure and integration, which are nicely connected to closely related topics such as bounded variations and absolutely continuous functions representations theorems for linear functionals, Sovolev spaces and distribution.” (Gareth Speight, Mathematical Reviews, October, 2018)​