Ergodic measures on compact metric spaces for isometric actions by inductively compact groups

2016/03/01 by Yanqi Qiu, Qiu, Yanqi
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Primary 37A25 #Probability (math.PR) #Secondary 28A33 #math.DS #math.PR #msc:28A33 #msc:37A25

paper · pdf · doi:10.48550/arxiv.1603.00268

6 pages

arxiv created 2016/03/01 · openalex publication_date 2016/03/01 · arxiv updated 2016/03/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We obtain a partial converse of Vershik's description of ergodic probability measures on a compact metric space with respect to an isometric action by an inductively compact group. This allows us to identify, in this setting, the set of ergodic probability measures with the set of weak limit points of orbital measures.

Related

• Weight Ergodic Theorems for Probability Measures on Locally Compact Groups
• Pointwise ergodic theorems for actions of groups
• Amenability, Optimal Transport and Abstract Ergodic Theorems
• Ergodic theorem in Hadamard spaces in terms of inductive means
• Pointwise convergence of ergodic averages of bounded measurable functions for amenable groups