On Baire measurability in spaces of continuous functions

TL;DR

This paper explores the properties of Baire measurability and the structure of certain probability measures in the space of continuous functions on compact spaces, focusing on the relationship between different topologies.

Contribution

It investigates the w*-sequential closure of finitely supported probabilities and the coincidence of Baire sigma-algebras in C(K), providing new insights into their measurability properties.

Findings

Characterization of w*-sequential closure of finitely supported probabilities

Conditions for Baire sigma-algebras to coincide in C(K)

Insights into measurability in spaces of continuous functions

Abstract

Let C(K) be the Banach space of all continuous functions on a given compact space K. We investigate the w*-sequential closure in C(K)* of the set of all finitely supported probabilities on K. We discuss the coincidence of the Baire sigma-algebras on C(K) associated to the weak and pointwise convergence topologies.