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 illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditional Riemann 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 functions rather 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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9780198501244

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...my appreciation? It is always a touchy discussion when debating about the use of the Riemann (or an analogous to) or the Lebesgue approach for a beginner's course on integration theory. My point of view is quite close to the one of the author so there will be no arguing here. To the others, let me just say the following: take the book in your hands, read (part of) it and you will see that it is reasonable and advisable to present a rigorous introduction of the Lebesgue integration theory to beginners. Belgian Mathematical Society Priestley takes a great deal of care to motivate you to grasp the concepts and introduces plenty of examples. New Scientist, 3 October 1998

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