On metrisation of the space of idempotent probability measures

TL;DR

This paper introduces a new metric for the space of idempotent probability measures on compact spaces, extending existing metrics and generating the pointwise convergence topology.

Contribution

The paper proposes a novel metric on the space of idempotent probability measures that aligns with the pointwise convergence topology, extending metrics from the underlying compact space.

Findings

The new metric extends the metrics on the compactum.

It generates the pointwise convergence topology.

The metric is compatible with the existing topology.

Abstract

In this paper we introduce a metrics on the space of idempotent probability measures on a given compactum, which extends the metrics on the compactum. It is proven the introduced metrics generates the pointwise convergence topology on the space of idempotent probability measures