AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
A Modern Theory of Integration
About this Title
Robert G. Bartle, Eastern Michigan University, Ypsilanti, MI
Publication: Graduate Studies in Mathematics
Publication Year:
2001; Volume 32
ISBNs: 978-0-8218-0845-0 (print); 978-1-4704-2086-4 (online)
DOI: https://doi.org/10.1090/gsm/032
MathSciNet review: MR1817647
MSC: Primary 26-01; Secondary 26A39
Table of Contents
Download chapters as PDF
Front/Back Matter
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