Furstenberg entropy values for nonsingular actions of groups without property (T)

Danilenko, Alexandre

doi:10.1090/proc/13278

Furstenberg entropy values for nonsingular actions of groups without property (T)
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Proc. Amer. Math. Soc. 145 (2017), 1153-1161 Request permission

Abstract:

Let $G$ be a discrete countable infinite group that does not have Kazhdan’s property (T) and let $\kappa$ be a generating probability measure on $G$. Then for each $t>0$, there is a type $III_1$ ergodic free nonsingular $G$-action whose $\kappa$-entropy (or the Furstenberg entropy) is $t$.

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