Book:H.A. Priestley/Introduction to Integration
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H.A. Priestley: Introduction to Complex Analysis
Published $\text {1997}$, Introduction to Integration
- ISBN 0-19-850123-4
Subject Matter
Contents
- Preface
- Notation
- 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
- Bibliography
- Notation index
- Subject index