Atomicity related to non-additive integrability

TL;DR

This paper explores Gould integrability of vector functions on atomic measure spaces and establishes a Radon-Nikodym theorem within this context, advancing the understanding of non-additive integrability.

Contribution

It introduces new results on Gould integrability for vector functions on atomic measure spaces and proves a Radon-Nikodym theorem in this setting.

Findings

Gould integrability characterized for vector functions on atomic measure spaces

Radon-Nikodym theorem established in the context of non-additive measures

Enhanced understanding of non-additive integrability in atomic spaces

Abstract

In this paper we present some results concerning Gould integrability of vector functions with respect to a monotone measure on finitely purely atomic measure spaces. As an application a Radon-Nikodym theorem in this setting is obtained.