Аннотация:The following question due to Thouvenot is well-known in ergodic theory.
Let $S$ and $T$ be automorphisms of a probability space and
$ S \times S $ be isomorphic to $T \times 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 of some flows.
We show that the isomorphism of weakly mixing flows $ S_t \times S_t $ and $ T_t \times T_t $
implies the isomorphism of
the flows $S_t$ and $T_t$, if the latter has an integral weak limit.