**AMS Chelsea Publishing**

Volume: 241;
1965;
312 pp;
Hardcover

MSC: Primary 28;
**Print ISBN: 978-0-8218-5328-3
Product Code: CHEL/241.H**

List Price: $51.00

Individual Member Price: $45.90

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# Measure and Integration

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*Sterling K. Berberian*

This highly flexible text is organized into two parts: Part I is suitable
for a one-semester course at the first-year graduate level, and the book
as a whole is suitable for a full-year course.

Part I treats the theory of measure and integration over abstract measure
spaces. Prerequisites are a familiarity with epsilon-delta arguments and
with the language of naive set theory (union, intersection, function). The
fundamental theorems of the subject are derived from first principles,
with details in full. Highlights include convergence theorems (monotone,
dominated), completeness of classical function spaces (Riesz-Fischer
theorem), product measures (Fubini's theorem), and signed measures
(Radon-Nikodym theorem).

Part II is more specialized; it includes regular measures on locally
compact spaces, the Riesz-Markoff theorem on the measure-theoretic
representation of positive linear forms, and Haar measure on a locally
compact group. The group algebra of a locally compact group is
constructed in the last chapter, by an especially transparent method that
minimizes measure-theoretic difficulties. Prerequisites for Part II
include Part I plus a course in general topology.

To quote from the Preface:

“Finally, I am under no illusions as to
originality, for the subject of measure theory is an old one which has
been worked over by many experts. My contribution can only be in
selection, arrangement, and emphasis. I am deeply indebted to Paul R.
Halmos, from whose textbook I first studied measure theory; I hope that
these pages may reflect their debt to his book without seeming to be
almost everywhere equal to it.”

#### Readership

Graduate students interested in teaching and learning the theory of measure and integration.