Superrigidity, measure equivalence, and weak Pinsker entropy

We show that the class $\\mathscr{B}$, of discrete groups which satisfy conclusion Popa’s cocycle superrigidity theorem for Bernoulli actions, is invariant under measure equivalence. generalize this to setting probability preserving (p.m.p.) groupoids, and as a consequence we deduce any nonamenable lattice in product two noncompact, locally compact second countable must belong $\\mathscr{B}$. also introduce measure-conjugacy called weak Pinsker entropy that, if $G$ group then an orbit-equivalence every essentially free p.m.p. action $G$.