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

Alexandre I. Danilenko

Published 2015-12-16Version 1

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 $t$.