Introduction to Integration

Paperback | June 1, 1997

byH. 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 illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditionalRiemann integral), intended for a first course in integration. This suffices for elementary applications, and serves as an introduction to the core of the book. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functionsrather than on measure. The book is designed primarily as an undergraduate or introductory graduate textbook. It is similar in style and level to Priestley's Introduction to complex analysis, for which it provides a companion volume, and is aimed at both pure and applied mathematicians.Prerequisites are the rudiments of integral calculus and a first course in real analysis.

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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 illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditionalRiemann integral), intended for a first course in...

Hilary Priestley is at University of Oxford.

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Format:PaperbackDimensions:318 pages, 9.21 × 6.14 × 0.71 inPublished:June 1, 1997Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198501234

ISBN - 13:9780198501237

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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 of 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. The Fourier transform34. Integration in probability theoryAppendix IAppendix IIBibliographyNotation indexSubject index

Editorial Reviews

This is a very readable and well-planned book, most suitable for all mathematics graduates. The emphasis is on practice with many applications in the later chapters.