Lectures on Choquet's Theorem

ISBN-13: 9783540418344 / Angielski / Miękka / 2001 / 130 str.

Robert R. Phelps; R. R. Phelps; Martin Jager

Opis

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.

Spis treści

Preface 1 Introduction. The Krein-Milman theorem as an integral representation theorem 2 Application of the Krein-Milman theorem to completely monotonic functions 3 Choquet's theorem: The metrizable case 4 The Choquet-Bishop-de Leeuw existence theorem 5 Applications to Rainwater's and Haydon's theorems 6 A new setting: The Choquet boundary 7 Applications of the Choquet boundary to resolvents 8 The Choquet boundary for uniform algebras 9 The Choquet boundary and approximation theory 10 Uniqueness of representing measures 11 Properties of the resultant map 12 Application to invariant and ergodic measures 13 A method for extending the representation theorems: Caps 14 A different method for extending the representation theorems 15 Orderings and dilations of measures 16 Additional Topics References Index of symbols Index