Ziemer Modern Real Analysis

2. Auflage 2017
ISBN: 978-3-319-64629-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 278, 382 Seiten, eBook

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Ziemer, William P.

Weitere Mitwirkende

Torres, Monica

Inhaltsverzeichnis

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.

Über Autor(innen)

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.