Weak mixing for nonsingular Bernoulli actions of countable groups

Alexandre I. Danilenko

Published 2018-07-16Version 1

Let $A$ be a finite set, $G$ a discrete countable infinite group and $(\mu_g)_{g\in G}$ a family of probability measures on $A$ such that $\inf_{g\in G}\min_{a\in A}\mu_g(a)>0$. It is shown (among other results) that if the Bernoulli shiftwise action of $G$ on the infinite product space $\bigotimes_{g\in G}(A,\mu_g)$ is nonsingular and conservative then it is weakly mixing. This answers in positive a question by Z.~Kosloff who proved recently a weaker version of this result for $G=\Bbb Z$.