A Modern Theory of Integration
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A Modern Theory of Integration: (Graduate Studies in Mathematics)

A Modern Theory of Integration: (Graduate Studies in Mathematics)


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About the Book

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.

Table of Contents:
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

About the Author :
Robert G. Bartle, Eastern Michigan University, Ypsilanti, MI, and University of Illinois, Urbana, IL

Review :
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 MATH


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Product Details
  • ISBN-13: 9781470479015
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Language: English
  • Series Title: Graduate Studies in Mathematics
  • ISBN-10: 147047901X
  • Publisher Date: 30 Nov 2001
  • Binding: Paperback
  • No of Pages: 458


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