On a metric on the space of idempotent probability measures

TL;DR

This paper introduces a new metric for the space of idempotent probability measures on compact spaces, serving as an analog to the Kantorovich metric used for traditional probability measures.

Contribution

It constructs an idempotent analog of the Kantorovich metric specifically for the space of idempotent probability measures on compacta.

Findings

The metric is well-defined and satisfies metric properties.

It provides a framework for analyzing idempotent probability measures.

The construction parallels classical probability measure metrics.

Abstract

In this paper we construct a metric on the space of idempotent probability measures on the given compactum, which is an idempotent analog of the Kantorovich metric on the space of probability measures.