A Modern Theory of Integration
Will be published approx. on 30. November 2001
Book
Paperback/Softback
458 pages
978-1-4704-7901-5 (ISBN)
Description
Presents a relative new theory. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately. From the top series published by the AMS.
Reviews / Votes
The book presents its subject in a pleasing, didactically surprising, and well worth reading exposition. The proofs are, as a rule, easily understandable and the significance of the theorems that are worked through is illustrated by means of numerous examples. It can be recommended as a self-study book to every student with a basic foundation in analysis. It is also very suitable as a supplementary text for a course on integration on $\mathbf{R}$. -- Translated fromJahresbericht der Deutschen Mathematiker-Vereinigung A comprehensive, beautifully written exposition of the Henstock-Kurzweil (gauge, Riemann complete) integral ... There is an abundant supply of exercises which serve to make this book an excellent choice for a text for a course which would contain an elementary introduction to modern integration theory. -- Zentralblatt MATHMore details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-7901-5 (9781470479015)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Robert G. Bartle, Eastern Michigan University, Ypsilanti, MI, and University of Illinois, Urbana, IL
Content
Part 1. Integration on compact intervals
Chapter 1. Gauges and integrals
Chapter 2. Some examples
Chapter 3. Basic properties of the integral
Chapter 4. The fundamental theorems of calculus
Chapter 5. The Saks-Henstock lemma
Chapter 6. Measurable functions
Chapter 7. Absolute integrability
Chapter 8. Convergence theorems
Chapter 9. Integrability and mean convergence
Chapter 10. Measure, measurability, and multipliers
Chapter 11. Modes of convergence
Chapter 12. Applications to calculus
Chapter 13. Substitution theorems
Chapter 14. Absolute continuity
Part 2. Integration on infinite intervals
Chapter 15. Introduction to Part 2
Chapter 16. Infinite intervals
Chapter 17. Further re-examination
Chapter 18. Measurable sets
Chapter 19. Measurable functions
Chapter 20. Sequences of functions
Appendixes
Appendix A. Limits superior and inferior
Appendix B. Unbounded sets and sequences
Appendix C. The arctangent lemma
Appendix D. Outer measure
Appendix E. Lebesgue's differentiation theorem
Appendix F. Vector spaces
Appendix G. Semimetric spaces
Appendix H. Riemann-Stieltjes integral
Appendix I. Normed linear spaces
Some partial solutions
Solutions Manual
Chapter 1. Gauges and integrals
Chapter 2. Some examples
Chapter 3. Basic properties of the integral
Chapter 4. The fundamental theorems of calculus
Chapter 5. The Saks-Henstock lemma
Chapter 6. Measurable functions
Chapter 7. Absolute integrability
Chapter 8. Convergence theorems
Chapter 9. Integrability and mean convergence
Chapter 10. Measure, measurability, and multipliers
Chapter 11. Modes of convergence
Chapter 12. Applications to calculus
Chapter 13. Substitution theorems
Chapter 14. Absolute continuity
Part 2. Integration on infinite intervals
Chapter 15. Introduction to Part 2
Chapter 16. Infinite intervals
Chapter 17. Further re-examination
Chapter 18. Measurable sets
Chapter 19. Measurable functions
Chapter 20. Sequences of functions
Appendixes
Appendix A. Limits superior and inferior
Appendix B. Unbounded sets and sequences
Appendix C. The arctangent lemma
Appendix D. Outer measure
Appendix E. Lebesgue's differentiation theorem
Appendix F. Vector spaces
Appendix G. Semimetric spaces
Appendix H. Riemann-Stieltjes integral
Appendix I. Normed linear spaces
Some partial solutions
Solutions Manual