
Preface  Table of Contents  Supplementary Material 
Graduate Studies in Mathematics 2011; 206 pp; hardcover Volume: 126 ISBN10: 0821869191 ISBN13: 9780821869192 List Price: US$53 Member Price: US$42.40 Order Code: GSM/126 See also: An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog  Terence Tao Measure Theory and Integration  Michael E Taylor  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 Carathéodory 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. Request an examination or desk copy. Readership Graduate students interested in analysis, in particular, measure theory. Reviews "The entire book is not just an introduction to measure theory as the title says but a lively dialogue on mathematics with a focus on measure theory."  Mahendra Nadkarni, Mathematical Reviews 


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