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 Title An Introduction to Measure Theory
 Author(s) Terrence Tao
 Publisher: American Mathematical Society (AMS), 2011; eBook (Preliminary Version, 2012)
 Permission: Author's preliminary version made available with permission of the publisher, the AMS.
 Hardcover 206 pages
 eBook Author's Preliminary Version, PDF (265 pages, 1.3 MB)
 Language: English
 ISBN10: 0821869191
 ISBN13: 9780821869192
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Book Description
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis.
The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Caratheodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory.
The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former.
The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problemsolving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
About the Author(s) Terrence Tao is an AustralianAmerican mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory.