Lectures on Choquet's Theorem
2nd Edition
Published on 8. May 2001
Book
Paperback/Softback
X, 130 pages
978-3-540-41834-4 (ISBN)
Description
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.
More details
Series
Edition
Second Edition 2001
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
X, 130 p.
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 8 mm
Weight
215 gr
ISBN-13
978-3-540-41834-4 (9783540418344)
DOI
10.1007/b76887
Schweitzer Classification
Content
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.