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＜電子ブック＞
Lectures on Choquet's Theorem / by Robert R. Phelps
(Lecture Notes in Mathematics. ISSN:16179692 ; 1757)

版	2nd ed. 2001.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2001
本文言語	英語
大きさ	X, 130 p : online resource
著者標目	*Phelps, Robert R author SpringerLink (Online service)
件　名	LCSH:Potential theory (Mathematics) LCSH:Functional analysis FREE:Potential Theory FREE:Functional Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b76887

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