Weight Ergodic Theorems for Probability Measures on Locally Compact Groups

TL;DR

This paper establishes weight ergodic theorems for strictly aperiodic probability measures on locally compact groups, expanding the understanding of ergodic behavior in non-abelian group settings.

Contribution

It introduces weight ergodic theorems specifically for strictly aperiodic measures on locally compact groups, a novel extension in ergodic theory.

Findings

Proves ergodic theorems for strictly aperiodic measures

Extends ergodic results to non-abelian locally compact groups

Provides new tools for analyzing measure dynamics on groups

Abstract

Let $G$ be a locally compact group with the left Haar measure $m_{G}$. A probability measure ${\mu}$ on $G$ is said to be strictly aperiodic if the support of ${\mu}$ is not contained in a proper closed left coset of $G$. In this paper, we prove weight ergodic theorems for strictly aperiodic measures.