TY  - BOOK
AU  - Bartle, G. Robert
TI  - A modern theory of integration
T2  - Graduate studies in mathematics
SN  - 9780821852156
AV  - QA312 
PY  - 2001///]
CY  - Providence, RI
PB  - American Mathematical Society
KW  - Mathematics
N1  - 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
N2  - This book gives an introduction to integration theory via the "generalized Riemann integral" due to Henstock and Kurzweil. The class of integrable functions coincides with those of Denjoy and Perron and includes all conditionally convergent improper integrals as well as the Lebesgue integrable functions. Using this general integral the author gives a full treatment of the Lebesgue integral on the line.

The book is designed for students of mathematics and of the natural sciences and economics. An understanding of elementary real analysis is assumed, but no familiarity with topology or measure theory is needed. The author provides many examples and a large collection of exercises—many with solutions.
UR  - https://www.ams.org/books/gsm/032/
ER  -