An Ergodic Result

TL;DR

This paper introduces a general ergodic scheme applicable to arbitrary sets and mappings, focusing on inverse limits of finite partitions to study ergodicity in a broad context.

Contribution

It presents a novel ergodic framework based on inverse limits of finite partitions, extending traditional ergodic theory to more general set structures.

Findings

Develops a general ergodic scheme for arbitrary sets and mappings.

Uses inverse limits of finite partitions to analyze ergodicity.

Provides a new perspective on ergodic properties beyond classical measure-based approaches.

Abstract

A rather general ergodic type scheme is presented on arbitrary sets X, as they are generated by arbitrary mappings T : X \longrightarrow X. The structures considered on X are given by suitable subsets of the set of all of its finite partitions. Ergodicity is studied not with respect to subsets of X, but with the {\it inverse limits} of families of finite partitions.