Positive entropy actions of countable groups factor onto Bernoulli shifts

TL;DR

This paper proves that free ergodic actions of countably infinite groups with positive entropy can factor onto all Bernoulli shifts of lesser or equal entropy, extending classical entropy results to broader group actions.

Contribution

It generalizes the Sinai factor theorem to all countably infinite groups using positive Rokhlin and sofic entropy.

Findings

Actions with positive entropy factor onto all lower-entropy Bernoulli shifts

Extension of classical entropy theorems to countably infinite groups

Broader applicability of entropy factorization results

Abstract

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory.