Table of Contents

1. Setting the scene
2. Preliminaries
3. Intervals and step functions
4. Integrals of step functions
5. Continuous functions on compact intervals
6. Techniques of Integration I
7. Approximations
8. Uniform convergence and power series
9. Building foundations
10. Null sets
11. Linc functions
12. The space L of integrable functions
13. Non-integrable functions
14. Convergence Theorems: MCT and DCT
15. Recognizing integrable functions I
16. Techniques of integration II
17. Sums and integrals
18. Recognizing integrable functions II
19. The Continuous DCT
20. Differentiation of integrals
21. Measurable functions
22. Measurable sets
23. The character of integrable functions
24. Integration vs. differentiation
25. Integrable functions on Rk
26. Fubini's Theorem and Tonelli's Theorem
27. Transformations of Rk
28. The spaces L1, L2 and Lp
29. Fourier series: pointwise convergence
30. Fourier series: convergence re-assessed
31. L2-spaces: orthogonal sequences
32. L2-spaces as Hilbert spaces
33. Fourier transforms
34. Integration in probability theory
Appendix I
Appendix II
Bibliography
Notation index
Subject index