Phelps R.R. Choquet's Theorem

Springer, 2001. — 123 p.Preface to First Edition
Preface to Second Edition
Introduction. 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
References
Index of symbols
Index