Some Properties of The Finitely Additive Vector Integral

TL;DR

This paper investigates properties of finitely additive vector integrals, exploring their representations and applications to vector martingale convergence and the non-compact Choquet theorem.

Contribution

It provides new results on the representation of finitely additive vector integrals and their applications in convergence and measure theory.

Findings

Representation results for finitely additive vector integrals

Applications to convergence of vector-valued martingales

Insights into the non-compact Choquet theorem

Abstract

We prove some results concerning the finitely additive, vector integral of Bochner and Pettis and their representation over a countably additive probability space. Applications to convergence of vector valued martingales and to the non compact Choquet theorem are provided.