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Hardcover ISBN:  9780821838051 
Product Code:  GSM/4 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470420666 
Product Code:  GSM/4.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821838051 
eBook ISBN:  9781470420666 
Product Code:  GSM/4.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 

Book DetailsGraduate Studies in MathematicsVolume: 4; 1994; 395 ppMSC: Primary 26; 28
This book provides an elementary, selfcontained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if \(F\) is differentiable on the interval \([a,b]\), then \(F'\) is integrable on \([a,b]\) and \(\int _a^b F'= F(b)  F(a)\). One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which \(F\) is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for firstyear graduate students who have background in real analysis.
ReadershipFirst year graduate students in mathematics.

Table of Contents

Chapters

Chapter 1. Lebesgue measure

Chapter 2. Measurable functions

Chapter 3. The Lebesgue integral

Chapter 4. Bounded variation and absolute continuity

Chapter 5. Darboux and Baire class one functions

Chapter 6. Functions of generalized bounded variation

Chapter 7. The Denjoy integral

Chapter 8. The Perron Integral

Chapter 9. The Henstock Integral

Chapter 10. The McShane Integral

Chapter 11. Equivalence of integrals

Chapter 12. Integration by parts

Chapter 13. Convergence theorems

Chapter 14. Approximate derivatives

Chapter 15. The Khintchine integral

Chapter 16. The approximately continuous Henstock integral

Chapter 17. The approximately continuous Perron integral

Solutions to Exercises


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This book provides an elementary, selfcontained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if \(F\) is differentiable on the interval \([a,b]\), then \(F'\) is integrable on \([a,b]\) and \(\int _a^b F'= F(b)  F(a)\). One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which \(F\) is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for firstyear graduate students who have background in real analysis.
First year graduate students in mathematics.

Chapters

Chapter 1. Lebesgue measure

Chapter 2. Measurable functions

Chapter 3. The Lebesgue integral

Chapter 4. Bounded variation and absolute continuity

Chapter 5. Darboux and Baire class one functions

Chapter 6. Functions of generalized bounded variation

Chapter 7. The Denjoy integral

Chapter 8. The Perron Integral

Chapter 9. The Henstock Integral

Chapter 10. The McShane Integral

Chapter 11. Equivalence of integrals

Chapter 12. Integration by parts

Chapter 13. Convergence theorems

Chapter 14. Approximate derivatives

Chapter 15. The Khintchine integral

Chapter 16. The approximately continuous Henstock integral

Chapter 17. The approximately continuous Perron integral

Solutions to Exercises