TL;DR
This paper investigates properties of Choquet maximal Radon probability measures on compact convex sets in locally convex spaces, providing foundational results for a subsequent non-separable C*-algebras Stone-Weierstrass theorem.
Contribution
It introduces new properties of Choquet maximal Radon measures and establishes a key theorem that supports a broader non-separable C*-algebras approximation theory.
Findings
Properties of Choquet maximal Radon measures are characterized.
Main theorem (Theorem 3.12) provides foundational measure-theoretic results.
Results are instrumental for a future non-separable C*-algebras Stone-Weierstrass theorem.
Abstract
The aim of this paper is to present some properties of Choquet maximal Radon probability measures on compact, convex subsets of Hausdorff, locally convex, topological real vector spaces. Theorem 3.12 is the main result of the paper. While somewhat technical, the results here are foundational for my proof of a Stone-Weierstrass theorem for non-separable C*-algebras, in the companion paper 'On the Stone-Weierstrass theorem'.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Mathematical Analysis and Transform Methods