Graduate Studies in Mathematics
Volume: 126;
2011;
206 pp;
Hardcover
MSC: Primary 28;
Print ISBN: 978-0-8218-6919-2
Product Code: GSM/126
List Price: $60.00
AMS Member Price: $48.00
MAA Member Price: $54.00
Electronic ISBN: 978-1-4704-1187-9
Product Code: GSM/126.E
List Price: $56.00
AMS Member Price: $44.80
MAA Member Price: $50.40
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Supplemental Materials
An Introduction to Measure Theory
Share this pageTerence Tao
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 problem-solving
strategies in analysis is also given. The last three sections discuss
optional topics related to the main matter of the book.
Readership
Graduate students interested in analysis, in particular, measure theory.
Reviews & Endorsements
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
Table of Contents
Table of Contents
An Introduction to Measure Theory
- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- Measure theory 118 free
- Related articles 173190
- Bibliography 201218
- Index 203220 free
- Back Cover Back Cover1226