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Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

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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 St ⊗ St and Tt ⊗ Tt are isomorphic, then so are the flows St and Tt, provided that one of them has a weak integral limit.

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Authors and Affiliations

  1. LomonosovMoscow State University, Moscow, 119991, Russia

    V. V. Ryzhikov

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  1. V. V. Ryzhikov
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Correspondence to V. V. Ryzhikov.

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Original Russian Text © V. V. Ryzhikov, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 6, pp. 912–917.

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Ryzhikov, V.V. Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows. Math Notes 104, 900–904 (2018). https://doi.org/10.1134/S0001434618110330

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