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The Integrals of Lebesgue, Denjoy, Perron, and Henstock
About this Title
Russell A. Gordon, Whitman College, Walla Walla, WA
Publication: Graduate Studies in Mathematics
Publication Year:
1994; Volume 4
ISBNs: 978-0-8218-3805-1 (print); 978-1-4704-2066-6 (online)
DOI: https://doi.org/10.1090/gsm/004
MathSciNet review: MR1288751
MSC: Primary 26A39; Secondary 26-01, 26A42, 28-02
Table of Contents
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Front/Back Matter
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