Introduction to Integration

Introduction to Integration

by H. A. Priestley
ISBN-10:
0198501234
ISBN-13:
9780198501237
Pub. Date:
12/04/1997
Publisher:
Oxford University Press
ISBN-10:
0198501234
ISBN-13:
9780198501237
Pub. Date:
12/04/1997
Publisher:
Oxford University Press
Introduction to Integration

Introduction to Integration

by H. A. Priestley

Paperback

$60.0
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Overview

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: 318
Product dimensions: 6.10(w) x 9.00(h) x 0.90(d)
Age Range: 4 - 8 Years

About the Author

Oxford University

Table of Contents

1. Setting the scene2. Preliminaries3. Intervals and step functions4. Integrals of step functions5. Continuous functions on compact intervals6. Techniques of Integration I7. Approximations8. Uniform convergence and power series9. Building foundations10. Null sets11. Linc functions12. The space L of integrable functions13. Non-integrable functions14. Convergence Theorems: MCT and DCT15. Recognizing integrable functions I16. Techniques of integration II17. Sums and integrals18. Recognizing integrable functions II19. The Continuous DCT20. Differentiation of integrals21. Measurable functions22. Measurable sets23. The character of integrable functions24. Integration vs. differentiation25. Integrable functions on Rk26. Fubini's Theorem and Tonelli's Theorem27. Transformations of Rk28. The spaces L1, L2 and Lp29. Fourier series: pointwise convergence30. Fourier series: convergence re-assessed31. L2-spaces: orthogonal sequences32. L2-spaces as Hilbert spaces33. Fourier transforms34. Integration in probability theoryAppendix IAppendix IIBibliographyNotation indexSubject index
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