A decomposition theorem for maxitive measures

TL;DR

This paper introduces a decomposition theorem for maxitive measures, showing they can be expressed as the supremum of a measure with density and a residual measure null on compact sets, enhancing understanding of their structure.

Contribution

It provides a novel decomposition theorem for maxitive measures, clarifying their structure and relation to measures with densities under certain conditions.

Findings

Maxitive measures can be decomposed into a measure with density and a residual measure.

The residual measure is null on compact sets under specific conditions.

This decomposition aids in analyzing the structure of maxitive measures.

Abstract

A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures can be decomposed as the supremum of a maxitive measure with density, and a residual maxitive measure that is null on compact sets under specific conditions.