On measures on Rosenthal compacta

TL;DR

This paper investigates Radon measures on Rosenthal compacta, demonstrating they are countably determined or of countable type under certain conditions, using caliber-type properties of measures.

Contribution

It provides new proofs and insights into the measure-theoretic properties of Rosenthal compacta, especially those representable by functions with countably many discontinuities.

Findings

Radon measures on certain Rosenthal compacta are countably determined.

Every Radon measure on an arbitrary Rosenthal compactum is of countable type.

The approach uses caliber-type properties of measures parameterized by separable metrizable spaces.

Abstract

We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every Radon measure on an arbitrary Rosenthal compactum is of countable type. Our approach is based on some caliber-type properties of measures, parameterized by separable metrizable spaces.