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

Published online by Cambridge University Press:  13 March 2018

B. MITCHELL BAKER ,
THIERRY GIORDANO  and
RADU B. MUNTEANU
B. MITCHELL BAKER
Affiliation:
Mathematics Department, U.S. Naval Academy, Chauvenet Hall, 572C Holloway Road, Annapolis, MD 21402-5002, USA email [email protected]
THIERRY GIORDANO
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N 6N5 email [email protected]
RADU B. MUNTEANU
Affiliation:
Department of Mathematics, University of Bucharest, 14 Academiei Street, 010014, Bucharest, Romania Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702, Bucharest, Romania email [email protected]
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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 Bernoulli measure is approximately transitive. We also extend the result to a larger class of probability measures.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 2881 - 2895
Copyright
© Cambridge University Press, 2018 

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