Representation of maxitive measures: an overview

TL;DR

This paper reviews and unifies various Radon--Nikodym type theorems for idempotent integration with maxitive measures, and introduces new related results, advancing the theoretical understanding of maxitive measure representation.

Contribution

It provides a comprehensive overview and unification of Radon--Nikodym theorems for maxitive measures and presents new theoretical results in this area.

Findings

Unified several Radon--Nikodym like theorems for maxitive measures

Proved new results related to idempotent integration

Enhanced the theoretical framework of maxitive measure representation

Abstract

Idempotent integration is an analogue of Lebesgue integration where $\sigma$-maxitive measures replace $\sigma$-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent integral, we also prove new results of the same kind.