A Version of Koml\'os Theorem for Additive Set Functions

TL;DR

This paper extends Komlós' theorem to finitely additive measures, establishing a subsequence principle and exploring applications in the context of additive set functions.

Contribution

It introduces a version of Komlós' theorem for finitely additive measures, broadening its applicability beyond random variables.

Findings

Established a subsequence principle for finitely additive measures

Provided applications demonstrating the theorem's utility

Extended classical results to a broader measure-theoretic setting

Abstract

We provide a version of the celebrated theorem of Koml\'os in which, rather then random quantities, a sequence of finitely additive measures is considered. We obtain a form of the subsequence principle and some applications.