A disintegration theorem

TL;DR

This paper introduces a novel measure disintegration method that removes the common separability assumption, leveraging recent spectral fiber results to broaden applicability in measure theory.

Contribution

It presents a new disintegration theorem that does not require separability, expanding the theoretical framework for measure decomposition.

Findings

Disintegration theorem without separability assumption

Utilizes spectral fiber results for measure analysis

Broadens measure theory applicability

Abstract

A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently by the first-named author.