Lebesgue Integration (Dover Books on Mathema 1.4tics)

Book Details:

• Publisher: Dover

• Author: J.H. Williamson

• Language: English

• ISBN: 9780486789774

• Cover: Paperback

• Binding: Paperback

• Edition: Reprint

• Release Date: 17-09-2014

• Number of Pages: 128

• Package Dimensions: 8.7 x 5.9 x 0.2 inches

About The Book:

This concise and self-contained introduction to Lebesgue integration is ideal for advanced undergraduate mathematics majors. It assumes a basic understanding of real variable theory and elementary calculus, and it serves as an accessible yet thorough treatment of Lebesgue integration.

The book covers fundamental concepts such as measurable sets, Lebesgue measure, and Borel sets, before moving on to more complex topics like convergence theorems, Fourier theory, and integrals of measurable functions. The exploration of the integral is divided into two parts, making it approachable for readers at various levels of mathematical maturity.

In addition to core integration topics, the text includes a chapter on calculus, focusing on change of variables, differentiation of integrals, and integration by parts. The book concludes with a discussion on general measures, including absolute continuity and convolution products, providing a comprehensive view of Lebesgue integration theory.

Each chapter contains exercises, ranging from simple to challenging, allowing students to solidify their understanding and enhance their problem-solving skills.