# Spaces of max-min measures on compact Hausdorff spaces

## TL;DR

This paper explores the properties of max-min measures on compact Hausdorff spaces, showing their functorial relationship to max-plus measures and analyzing the differences in their monads.

## Contribution

It establishes an isomorphism between the functors of max-min and max-plus measures, and investigates the non-isomorphism of their monads.

## Key findings

- Max-min measure functor is isomorphic to max-plus measure functor.
- Monads generated by these functors are not isomorphic.
- Provides insights into the structure of measures on compact Hausdorff spaces.

## Abstract

The notion of max-min measure is a counterpart of the notion of max-plus measure (Maslov measure or idempotent measure). In this paper we consider the spaces of max-min measures on the compact Hausdorff spaces. It is proved that the obtained functor of max-min measures is isomorphic to the functor of max-plus (idempotent) measures considered by the second-named author. However, it turns out that the monads generated by these functors are not isomorphic.