The unique ergodicity of equicontinuous laminations

TL;DR

This paper proves that transversely equicontinuous minimal laminations on locally compact spaces have a transversely invariant Radon measure, which is unique up to scaling in the compact case, advancing understanding of invariant measures in lamination theory.

Contribution

It establishes the existence and uniqueness of transversely invariant Radon measures for transversely equicontinuous minimal laminations, a novel result in lamination dynamics.

Findings

Existence of transversely invariant Radon measure for such laminations.

Uniqueness of the measure in the compact case.

Extension of measure theory in lamination contexts.

Abstract

We prove that a transversely equicontinuous minimal lamination on a locally compact metric space $Z$ has a transversely invariant Radon measure. Moreover if the space $Z$ is compact, then the tranversely invariant Radon measure is shown to be unique up to a scaling.