Book:H.A. Priestley/Introduction to Integration

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H.A. Priestley: Introduction to Complex Analysis

Published $1997$, Introduction to Integration

ISBN 0-19-850123-4.

Subject Matter



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. $\text L^{\text{inc} }$ functions
12. The class $\text L$ 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 $\R^k$
26. Fubini's Theorem and Tonelli's Theorem
27. Transformations of $\R^k$
28. The spaces $\text L^1$, $\text L^2$, and $\text L^p$
29. Fourier series: pointwise convergence
30. Fourier series: convergence reassessed
31. $\text L^2$-spaces: orthogonal sequences
32. $\text L^2$-spaces as Hilbert spaces
33. Fourier transforms
34. Integration in probability theory
Appendix I: historical remarks
Appendix II: reference
Notation index
Subject index