An Introduction to Lebesgue Integration and Fourier Series

by Howard J. Wilcox, David L. Myers

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects.
The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire.
Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Genres: Mathematics, Reference

192 pages, Paperback

First published January 1, 1978

Reviews

[Leonhard Euler · Rating 3 out of 5]

Worth reading depending on who you are and what you want. If you're a graduate student trying to learn analysis you'd be better off with a proper graduate analysis book like Rudin's (as limited as it is). If you're an undergraduate trying to peer at jewels in your neighbor's house through stained glass you might find it appropriate, given that it only develops measure as Lebesgue measure on the real line with hardly a mention of sigma algebras or Borel sets or general measures or anything like that. Given that I'm using it as a brief reminder of what graduate analysis is all about it mostly served its purpose, but I'll probably stick to looking through Folland in the future.