An Introduction to Lebesgue Integration and Fourier Series

Howard J. Wilcox

The author wanted to provide Lebesgue integration and the Fourier series on an undergraduate level because most undergraduate texts either do not cover this material or do so in a very superficial fashion. This ambition led to the creation of this book. The end product is an introduction that is easy to understand, succinct, and well-organized. Some topics covered include 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 topics.

The authors not only cover these topics in a helpful and comprehensive way, but they have also made an effort to motivate the student by keeping the theory goals always in sight and justifying each step of the development in terms of those goals. The authors cover these topics in such a way and have also made an effort to motivate the student. In addition, connections are made between new ideas and ideas that are already part of the student’s repertoire wherever possible.

In conclusion, the text is supplemented with many examples and activities so that readers can evaluate how well they understand the subject matter. Students majoring in mathematics, engineering, and science will find this to be an excellent treatment that has been well thought through and is presented in a manner suitable for a one-semester course. The only need that must be met is a fundamental understanding of advanced calculus, which should include an understanding of compactness, continuity, uniform convergence, and Riemann integration.