When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: §2.2.5 and §8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in §7.3.2, the author has added 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 N 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.

Solutions manual is available to instructors who adopt the textbook for their course Second edition revised with new topics, some reworked text, new exercises Suitable for a one-semester graduate course in integration theory as well as for independent study Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

Autorentext
Daniel W. Stroock is Professor Emeritus of Mathematics at MIT. Professor Stroock's research interests focus on probability theory and stochastic processes. Stroock (with S. Varadhan) was awarded the Leroy P. Steele Prize for seminal contributions to research in stochastic equations. In 2007, Stroock received an Honorary Fellowship at Swansea University, Wales, and in 2004 selected to be Foreign Member of the Polish Academy of Arts and Sciences. Professor Stroock is a Fellow of the American Academy of Arts and Sciences (1991), and a Member of the National Academy of Sciences (1995). Professor Stroock has made many contributions to pedagogical literature, among these include: An Introduction to Markov Processes" (GTM 230), "Essentials of Integration Theory for Analysis" (GTM 262), "Multidimensional Diffusion Processes" (Classics in Mathematics).

Inhalt
Preface.- Notation.- 1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. RadonNikodym, Hahn, Daniell Integration, and Carathéodory- Index.