Hardcover ISBN:  9780821806142 
Product Code:  SURV/54 
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eBook ISBN:  9780821832141 
Product Code:  SURV/54.E 
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AMS Member Price:  $100.00 
Hardcover ISBN:  9780821806142 
eBook: ISBN:  9780821832141 
Product Code:  SURV/54.B 
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MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9780821806142 
Product Code:  SURV/54 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9780821832141 
Product Code:  SURV/54.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821806142 
eBook ISBN:  9780821832141 
Product Code:  SURV/54.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 54; 1997; 216 ppMSC: Primary 26; 28; 42; 54; Secondary 30; 40; 49
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 settheoretic topology.
 Gives unified treatments of large bodies of research found in the literature.
ReadershipGraduate students, research mathematicians and engineers interested in real functions.

Table of Contents

Chapters

1. Subsets of $\mathbb {R}$

2. Baire class 1

3. Differentiability classes

4. The derivative function

5. BiLipschitzian homeomorphisms

6. Approximation by homeomorphisms

7. Measures on $\mathbb {R}^n$

8. Blumberg’s theorem

9. Improving the behavior of Fourier series

10. Preservation of convergence of Fourier series

11. Fourier series of integrable functions


Reviews

[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


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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 settheoretic topology.
 Gives unified treatments of large bodies of research found in the literature.
Graduate students, research mathematicians and engineers interested in real functions.

Chapters

1. Subsets of $\mathbb {R}$

2. Baire class 1

3. Differentiability classes

4. The derivative function

5. BiLipschitzian homeomorphisms

6. Approximation by homeomorphisms

7. Measures on $\mathbb {R}^n$

8. Blumberg’s theorem

9. Improving the behavior of Fourier series

10. Preservation of convergence of Fourier series

11. Fourier series of integrable functions

[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