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

B. Mitchell Baker; Thierry Giordano; Radu B. Munteanu

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arXiv · 1707.00927

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

B. Mitchell Baker·Thierry Giordano·Radu B. Munteanu

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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.

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B. Mitchell Baker, Thierry Giordano, Radu B. Munteanu. 2017-07-04. Approximate transitivity of the ergodic action of the group of finite permutations of $\mathbb{N}$ on $\{0, 1 \}^{\mathbb{N}}$. https://arxiv.org/abs/1707.00927

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