Essentials of Integration Theory for Analysis

This second edition of the textbook is a substantial revision of the best-selling Birkhäuser title, A Concise Introduction to the Theory of Integration. It is appropriate for a one-semester graduate course in integration theory and for independent study. It has been revised with new topics, a complete solutions manual, and new exercises.

Format: Hardback
Length: 285 pages
Publication date: 24 November 2020
Publisher: Springer Nature Switzerland AG

When the initial edition of this textbook was published in 2011, it represented a significant revision of the highly acclaimed Birkhäuser title authored by the same author, A Concise Introduction to the Theory of Integration. Suitable as a primary text for a one-semester graduate course in integration theory, this GTM is also valuable for independent study. A comprehensive solutions manual is available for instructors who adopt the text for their courses.

This second edition has undergone revisions as follows: §2.2.5 and §8.3 have been extensively reworked. Several new topics have been introduced. As an application of the material concerning Hermite functions in §7.3.2, the author has included a brief introduction to Schwartz's theory of tempered distributions in §7.3.4. Section §7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections §8.2.5 and §8.2.6, where Lévy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on ℝN are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material.

Weight: 640g
Dimension: 161 x 240 x 23 (mm)
ISBN-13: 9783030584771
Edition number: 2nd ed. 2020