L^1 Ergodic Theorems for Random Group Averages

TL;DR

This paper establishes an L^1 ergodic theorem for averages derived from independent random selectors within general measure-preserving group actions, extending previous work to more general and sparse random subsequences.

Contribution

It introduces a more general L^1 ergodic theorem for random group averages, broadening the scope of previous results to include sparse random subsequences in measure-preserving actions.

Findings

Proves an L^1 ergodic theorem for random group averages.

Extends ergodic theorems to sparse random subsequences.

Applicable to general measure-preserving group actions.

Abstract

This is an earlier, but more general, version of "An L^1 Ergodic Theorem for Sparse Random Subsequences". We prove an L^1 ergodic theorem for averages defined by independent random selector variables, in a setting of general measure-preserving group actions. A far more readable version of this paper is in the works.