Contents

Preface

Part 1. Integration on compact intervals

1. Gauges and integrals

2. Some examples

3. Basic properties of the integral

4. The Fundamental Theorems of Calculus

5. The Saks-Henstock lemma

6. Measurable functions

7. Absolute integrability

8. Convergence theorems

9. Integrability and mean convergence

10. Measure, measurability and multipliers

11. Modes of convergence

12. Applications to calculus

13. Substitution theorems

14. Absolute continuity

Part 2. Integration on infinite intervals

15. Introduction to Part 2

16. Infinite intervals

17. Further re-examination