Conglomerability and Finitely Additive Representations

TL;DR

This paper explores the concept of conglomerability and its role in representing distributions through random quantities, highlighting its significance in probability and analysis.

Contribution

It establishes new results linking conglomerability to the existence of finitely additive representations of distributions.

Findings

Conglomerability is crucial for representing distributions with finitely additive measures.

The paper demonstrates applications of conglomerability in probability theory.

Results connect conglomerability to analytical properties of measures.

Abstract

We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study finitely additive conditional probability. We show that this property has many interesting applications in probability as well as in analysis.