Essentials of Integration Theory for Analysis

This textbook offers a thorough exploration of integration theory, making it ideal for graduate-level study. Essentials of Integration Theory for Analysis includes significant revisions and new topics.

The textbook Essentials of Integration Theory for Analysis serves as a comprehensive resource for graduate students delving into integration theory. First published in 2011, it represented a significant revision of a previous best-selling title by the same author. This edition is structured to support a one-semester graduate course, making it an ideal primary text. Additionally, it is designed for independent study, appealing to those seeking to deepen their understanding of the subject matter. Instructors adopting the textbook will find a complete solutions manual available, enhancing the learning experience for their students.

In this second edition of Essentials of Integration Theory for Analysis, notable revisions have been made to enhance clarity and depth. Sections 2.2.5 and 8.3 have undergone substantial reworking, and new topics have been introduced to enrich the content. A significant addition is the brief introduction to Schwartz's theory of tempered distributions, which complements the material on Hermite functions. Furthermore, a completely new section, 7.4, explores applications of Fourier analysis to measures, including the Central Limit Theorem, thereby providing practical insights into the theory.

Additional enhancements include new subsections that prove Lévy's Continuity Theorem and Bochner's characterization of Fourier transforms of Borel probability measures. The inclusion of new exercises, some based on previously covered material and others on newly introduced topics, ensures that students are well-equipped to apply their knowledge effectively. This revised edition stands as a valuable tool for both educators and students in the field of integration theory.