Geodesic
Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows
Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 912-917.

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Let $S$ and $T$ be automorphisms of a probability space whose powers $S \otimes S$ and $T \otimes T$ isomorphic. Are the automorphisms $S$ and $T$ isomorphic? This 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 $S_t \otimes S_t$ and $T_t \otimes T_t$ are isomorphic, then so are the flows $S_t$ and $T_t$, provided that one of them has a weak integral limit.
Keywords: flow with invariant measure, weak closure, tensor power of a dynamical system, metric isomorphism. 
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V. V. Ryzhikov. Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows. Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 912-917. http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a8/

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