# Ergodicity via continuity

## TL;DR

This paper establishes a novel characterization of ergodicity for aperiodic automorphisms of Lebesgue spaces through the continuity of a specific map on a metric Boolean algebra, also extending to periodic and totally ergodic cases.

## Contribution

It introduces a new equivalence between ergodicity and map continuity on Boolean algebras, providing a fresh perspective on ergodic theory.

## Key findings

- Ergodicity is equivalent to the continuity of a certain map on a metric Boolean algebra.
- A related characterization is provided for periodic and totally ergodic transformations.
- The results unify different types of transformations under a common framework.

## Abstract

We show that the ergodicity of an aperiodic automorphism of a Lebesgue space is equivalent to the continuity of a certain map on a metric Boolean algebra. A related characterization is also presented for periodic and totally ergodic transformations