Lectures on Choquet's Theorem
Appearing for the first time in book form are the main results centered about Choquet's integral representation theorem-an important recent chapter in functional analysis. This theorem has applications to analysis, probability, potential theory, and functional analysis; it will doubtless have further applications as it becomes better known. This readable book presupposes a knowledge of integration theory and elementary functional analysis, including the Krein-Milman theorem and the Riesz representation theorem. --Back cover.
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Section Page 1 Introduction The KreinMilman theorem as an integral representation theorem
Application of the KreinMilman theorem to completely monotonic functions
The metrizable case
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affine function apply assertion Baire set Baire subsets Bishop-de Leeuw Borel measure Borel set CC(Y choose Choquet boundary closed convex cone closed convex hull compact base compact convex set compact convex subset compact Hausdorff space compact set compact subset continuous functions continuous linear functional convex combination convex cone convex set Corollary countable defined definition denote dense disjoint element ergodic measures exists a unique extreme points extreme ray f in C(X fact fi(f func function algebra function f Furthermore greatest lower bound Hausdorff space hence homeomorphic implies invariant probability measures Krein-Milman theorem lattice Lebesgue lemma lim inf locally convex space maximal measure measure f i metrizable nonempty nonnegative measure peak points probability measure Proposition 3.1 prove representation theorem representing measures result Riesz theorem separates points sequence set of extreme simplex Suppose tion topology universal cap upper semicontinuous weak