2 problems

Let $G$ be a countably infinite group, let $G \curvearrowright (X,\mu)$ be a free probability-measure-preserving action, and let $\Gamma\leq G$ be a finite-index subgroup. Subgroup…

Let $G \curvearrowright (X,\mu)$ and $G \curvearrowright (Y,\nu)$ be free probability-measure-preserving actions, and let $\mu\times\nu$ be their direct-product joining. Direct-pro…