Modern Real Analysis / by William P. Ziemer.

Format:

Book

Author/Creator:

Ziemer, William P., Author.

Series:

Graduate Texts in Mathematics, 0072-5285 ; 278

Language:

English

Subjects (All):

Functions of real variables.

Functional analysis.

Measure theory.

Real Functions.

Functional Analysis.

Measure and Integration.

Local Subjects:

Real Functions.

Functional Analysis.

Measure and Integration.

Physical Description:

1 online resource (XI, 382 p.)

Edition:

2nd ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

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 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. .

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.

ISBN:

3-319-64629-X