Bibliographic Information

Modern real analysis

William P. Ziemer ; with contributions by Monica Torres

(Graduate texts in mathematics, v. 278)

Springer, c2017

2nd ed

Available at  / 48 libraries

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Note

1st ed. published: PWS Pub. , c1995

Includes bibliographical references (p. 375-377) and index

Description and Table of Contents

Description

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.

Table of 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.

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Details

  • NCID
    BB25233677
  • ISBN
    • 9783319646282
  • LCCN
    2017949128
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xi, 382 p.
  • Size
    25 cm
  • Parent Bibliography ID
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