Lectures on Choquet's Theorem

• Κύριος συγγραφέας: Phelps, Robert R. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Έκδοση: 2nd ed. 2001.
• Σειρά: Lecture Notes in Mathematics, 1757
• Θέματα: Potential theory (Mathematics).; Functional analysis.; Potential Theory.; Functional Analysis.

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...

Πίνακας περιεχομένων:

• 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.