Overview
- 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 262)
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Table of contents (8 chapters)
Keywords
About this book
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 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.
Authors and Affiliations
About the author
Daniel W. Stroock is Emeritus professor of mathematics at MIT. He is a respected mathematician in the areas of analysis, probability theory and stochastic processes. Prof. Stroock has had an active career in both the research and education. From 2002 until 2006, he was the first holder of the second Simons Professorship of Mathematics. In addition, he has held several administrative posts, some within the university and others outside. In 1996, the AMS awarded him together with his former colleague jointly S.R.S. Varadhan the Leroy P. Steele Prize for seminal contributions to research in stochastic processes. Finally, he is a member of both the American Academy of Arts and Sciences, the National Academy of Sciences and a foreign member of the Polish Academy of Arts and Sciences.
Bibliographic Information
Book Title: Essentials of Integration Theory for Analysis
Authors: Daniel W. Stroock
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-58478-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-58477-1Published: 24 November 2020
Softcover ISBN: 978-3-030-58480-1Published: 25 November 2021
eBook ISBN: 978-3-030-58478-8Published: 24 November 2020
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XVI, 285
Number of Illustrations: 1 b/w illustrations
Topics: Measure and Integration, Analysis