Pub. Date:
Oxford University Press
Introduction to Integration

Introduction to Integration

by H. A. PriestleyH. A. Priestley


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Introduction to Integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of examples and exercises. Intended as a first course in integration theory for students familiar with real analysis, the book begins with a simplified Lebesgue integral, which is then developed to provide an entry point for important results in the field. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measures. Designed as an undergraduate or graduate textbook, it is a companion volume to the author's Introduction to Complex Analysis and is aimed at both pure and applied mathematicians.

Product Details

ISBN-13: 9780198501237
Publisher: Oxford University Press
Publication date: 12/04/1997
Pages: 320
Product dimensions: 6.10(w) x 9.00(h) x 0.90(d)
Age Range: 4 - 8 Years

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
Notation index
Subject index

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