Modern Real Analysis

Softcover Nachdruck of the original 2. Auflage 2017
ISBN: 978-3-319-87840-9
Verlag: Springer International Publishing

Buch, Englisch, Band 278, 382 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 598 g

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

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

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.