Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

Abstract

Let S and T be automorphisms of a probability space whose powers S ⊗ S and T ⊗ T isomorphic. Are the automorphisms S and T isomorphičThis question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows S_t ⊗ S_t and T_t ⊗ T_t are isomorphic, then so are the flows S_t and T_t, provided that one of them has a weak integral limit.