Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Phelps, Robert R. (1926-2013)
Titre(s) : Lectures on Choquet's theorem [Texte électronique] / Robert R. Phelps
Édition : 2nd ed.
Publication : Berlin ; New York : Springer, cop. 2001
Description matérielle : 1 online resource (124 pages)
Collection : Lecture notes in mathematics ; 1757
Note(s) : Previous edition: Princeton, N.J. : Van Nostrand, 1966. - Includes bibliographical references (pages 115-121) and index. - Print version record.
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
Sujet(s) : Choquet, Théorie de
Indice(s) Dewey :
510 (23e éd.) = Mathématiques ; 515.73 (23e éd.) = Espaces vectoriels topologiques
Identifiants, prix et caractéristiques : ISBN 9783540487197
Identifiant de la notice : ark:/12148/cb446929795
Notice n° :
FRBNF44692979
(notice reprise d'un réservoir extérieur)
Table des matières : 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.
