Spaces of idempotent measures of compact metric spaces

TL;DR

This paper explores the geometric structure of spaces of idempotent measures on compact metric spaces, establishing that for infinite spaces, these measure spaces are topologically equivalent to the Hilbert cube.

Contribution

It proves that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube, revealing its geometric structure.

Findings

Space of idempotent measures on infinite compact metric spaces is homeomorphic to the Hilbert cube.

Provides new insights into the topology of measure spaces in metric geometry.

Enhances understanding of geometric properties of measure spaces.

Abstract

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.