Fr. 56.50

Lectures on Choquet's Theorem

English · Paperback / Softback

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Description

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A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.

List of contents

The Krein-Milman theorem as an integral representation theorem.- Application of the Krein-Milman theorem to completely monotonic functions.- Choquet's theorem: The metrizable case..- The Choquet-Bishop-de Leeuw existence theorem.- Applications to Rainwater's and Haydon's theorems.- A new setting: The Choquet boundary.- Applications of the Choquet boundary to resolvents.- The Choquet boundary for uniform algebras.- The Choquet boundary and approximation theory.- Uniqueness of representing measures..- Properties of the resultant map.- Application to invariant and ergodic measures.- A method for extending the representation theorems: Caps.- A different method for extending the representation theorems.- Orderings and dilations of measures.- Additional Topics.

Summary

A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.

Product details

Authors Robert R Phelps, Robert R. Phelps
Publisher Springer, Berlin
 
Languages English
Product format Paperback / Softback
Released 26.06.2009
 
EAN 9783540418344
ISBN 978-3-540-41834-4
No. of pages 130
Dimensions 156 mm x 236 mm x 10 mm
Weight 235 g
Illustrations X, 130 p.
Series Lecture Notes in Mathematics
Lecture Notes in Mathematics
Subjects Natural sciences, medicine, IT, technology > Mathematics > Analysis

set, B, Form, Integral, Function, Funktionalanalysis und Abwandlungen, Presentation, Theorem, Mathematics and Statistics, Functional Analysis, Ergodic theory, Functional analysis & transforms, Potential Theory, Potential theory (Mathematics), representing measures, metrizable

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