Overview
- Provides a foundation for further study in partial differential equations
- Completely self-contained text equips readers with the fundamentals of graduate real analysis
- New edition extensively revised and updated
- Supplies frequent opportunities to practice techniques
Part of the book series: Graduate Texts in Mathematics (GTM, volume 278)
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Table of contents (11 chapters)
Keywords
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
About the author
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
Book Title: Modern Real Analysis
Authors: William P. Ziemer
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-64629-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-64628-2Published: 19 December 2017
Softcover ISBN: 978-3-319-87840-9Published: 31 August 2018
eBook ISBN: 978-3-319-64629-9Published: 30 November 2017
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XI, 382
Topics: Real Functions, Functional Analysis, Measure and Integration