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Modern real analysis

Author: William P Ziemer
Publisher: Cham : Springer, 2017.
Series: Graduate texts in mathematics, 278.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ziemer, William P.
Modern real analysis.
Cham : Springer, 2017
(OCoLC)992784712
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: William P Ziemer
ISBN: 9783319646299 331964629X
OCLC Number: 1014337124
Description: 1 online resource (xi, 382 pages)
Contents: Preface --
1. Preliminaries --
2. Real, Cardinal and Ordinal Numbers --
3. Elements of Topology --
4. Measure Theory --
5. Measurable Functions --
6. Integration --
7. Differentiation --
8. Elements of Functional Analysis --
9. Measures and Linear Functionals --
10. Distributions --
11. Functions of Several Variables --
Bibliography --
Index.
Series Title: Graduate texts in mathematics, 278.
Responsibility: William P. Ziemer ; with contributions by Monica Torres.

Abstract:

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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"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 Read more...

 
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