Approximate transitivity of the ergodic action of the group of finite permutations of $\mathbb{N}$ on $\{0, 1 \}^{\mathbb{N}}$

Abstract

In this paper we show that the natural action of the symmetric group acting on the product space $\{0, 1 \}^{\mathbb{N}} $ endowed with a symmetric measure is approximately transitive. We also extend the result to a larger class of probability measures.