**Mathematical Surveys and Monographs**

Volume: 54;
1997;
216 pp;
Hardcover

MSC: Primary 26; 28; 42; 54;
Secondary 30; 40; 49

Print ISBN: 978-0-8218-0614-2

Product Code: SURV/54

List Price: $89.00

AMS Member Price: $71.20

MAA member Price: $80.10

**Electronic ISBN: 978-0-8218-3214-1
Product Code: SURV/54.E**

List Price: $89.00

AMS Member Price: $71.20

MAA member Price: $80.10

# Homeomorphisms in Analysis

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*Casper Goffman; Togo Nishiura; Daniel Waterman*

This book features the interplay of two main branches of mathematics: topology
and real analysis. The material of the book is largely contained in the
research publications of the authors and their students from the past 50
years. Parts of analysis are touched upon in a unique way, for example,
Lebesgue measurability, Baire classes of functions, differentiability, \(C^n\)
and \(C^{\infty}\) functions, the Blumberg theorem, bounded variation in the sense
of Cesari, and various theorems on Fourier series and generalized bounded
variation of a function.

Features:

- Contains new results and complete proofs of some known results for the first time.
- Demonstrates the wide applicability of certain basic notions and techniques in measure theory and set-theoretic topology.
- Gives unified treatments of large bodies of research found in the literature.

#### Readership

Graduate students, research mathematicians and engineers interested in real functions.

#### Reviews & Endorsements

[T]he book is an extensive survey on the results in analysis which concern homeomorphisms. The material is presented in a clear form. Proofs of longer theorems are usually broken down into lemmas. Many examples and comments further facilitate the reading. The text is rounded off with an appendix consisting of supplementary material, an extensive bibliography on the subject, and an index.

-- Mathematical Reviews

The book is well written, packed with information and makes a novel contribution to the literature. Much of what is in the book is important material that is now for the first time readily accessible … readers will appreciate the many comments that provide historical or motivational perspectives.

-- Professor Andrew Bruckner, University of California, Santa Barbara

[This] is, overall, an excellent book, of a type which, in this reviewer's opinion, is sorely lacking in mathematics these days.

-- Bulletin of the London Mathematical Society

#### Table of Contents

# Table of Contents

## Homeomorphisms in Analysis

- Contents vii10 free
- Preface xi14 free
- The one dimensional case xi14
- Mappings and measures on R[sup(n)] xii15 free
- Fourier series xiii16 free
- Part 1. The One Dimensional Case 118 free
- Part 2. Mappings and Measures on R[sup(n)] 5976
- Part 3. Fourier Series 109126
- Appendix A. Supplementary Material 187204
- Bibliography 207224
- Index 213230