An introduction to measure theory
 Author/Creator
 Tao, Terence, 1975
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2011.
 Physical description
 xvi, 206 p. : ill. ; 26 cm.
 Series
 Graduate studies in mathematics ; v. 126.
Access
Available online
Course reserve
 Course
 MATH205A01  Real Analysis
 Instructor(s)
 Ryzhik, Leonid

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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 201) and index.
 Publisher's Summary
 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 Radamacher 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 emphasised. 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..
(source: Nielsen Book Data)
Subjects
 Subject
 Measure theory.
 Measure and integration  Classical measure theory  Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence.
 Measure and integration  Classical measure theory  Integration with respect to measures and other set functions.
 Measure and integration  Classical measure theory  Measures and integrals in product spaces.
Bibliographic information
 Publication date
 2011
 Responsibility
 Terence Tao.
 Series
 Graduate studies in mathematics ; v. 126
 ISBN
 9780821869192
 0821869191