Overview

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.

Full Product Details

Author:   Robert R. Phelps
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Second Edition 2001
Volume:   1757
Dimensions:   Width: 15.20cm , Height: 0.70cm , Length: 22.90cm
Weight:   0.460kg
ISBN:  

9783540418344

ISBN 10:   3540418342
Pages:   130
Publication Date:   08 May 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table 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.

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