TY - JOUR
T1 - Bernoulli actions are weakly contained in any free action
AU - Abért, Miklós
AU - Weiss, Benjamin
PY - 2013/4
Y1 - 2013/4
N2 - Let Γ be a countable group and let f be a free probability measure-preserving action of Γ. We show that all Bernoulli actions of Γ are weakly contained in f. It follows that for a finitely generated group Γ, the cost is maximal on Bernoulli actions for Γ and that all free factors of i.i.d. (independent and identically distributed) actions of Γ have the same cost. We also show that if f is ergodic, but not strongly ergodic, then f is weakly equivalent to f×I, where Idenotes the trivial action of Γ on the unit interval. This leads to a relative version of the Glasner-Weiss dichotomy.
AB - Let Γ be a countable group and let f be a free probability measure-preserving action of Γ. We show that all Bernoulli actions of Γ are weakly contained in f. It follows that for a finitely generated group Γ, the cost is maximal on Bernoulli actions for Γ and that all free factors of i.i.d. (independent and identically distributed) actions of Γ have the same cost. We also show that if f is ergodic, but not strongly ergodic, then f is weakly equivalent to f×I, where Idenotes the trivial action of Γ on the unit interval. This leads to a relative version of the Glasner-Weiss dichotomy.
UR - http://www.scopus.com/inward/record.url?scp=84877964034&partnerID=8YFLogxK
U2 - 10.1017/S0143385711000988
DO - 10.1017/S0143385711000988
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AN - SCOPUS:84877964034
SN - 0143-3857
VL - 33
SP - 323
EP - 333
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -