Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

Abstract

Key words. Measure-preserving flows, tensor powers of dynamical systems, measure-theoretical isomorphism. AbstractThe following question due to Thouvenot is well-known in ergodic theory. Let S and T be automorphisms of a probability space and S ⊗ S be isomorphic to T ⊗ T . Will S and T be isomorphic? Our note contains a simple answer to this question and a generalization of Kulaga's result on the corresponding isomorphism within a class of flows. We show that the isomorphism of weakly mixing flows S t ⊗ S t and T t ⊗ T t implies the isomorphism of the flows S t and T t , if one of them has an integral weak limit.