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Catalogue Information
Field name	Details
Dewey Class	515.96
Title	Lectures on Choquet’s Theorem ([EBook] /) / edited by Robert R. Phelps.
Added Personal Name	Phelps, Robert R. editor.
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg, , 2001.
Physical Details	X, 130 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1757
ISBN	9783540487197
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b76887
Links to Related Works	Subject References: Functional Analysis . Mathematics . Potential Theory . Potential theory (Mathematics) . Authors: Phelps, Robert R. . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515.96 .

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Lectures on Choquet’s Theorem

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