Conjecture: In general a mixing transformation is not two-fold mixing. (English) Zbl 0574.28012

In this paper an attempt to solve an old problem whether a mixing transformation is two-fold mixing is made. A new topology in the space of all automorphisms of a Lebesgue space is introduced. In this topology the subspace of mixing automorphisms is a Baire space. Next, under the assumption of the validity of some conjecture, it is shown that the two- fold mixing automorphisms are of first category in the mixing ones. Hence, there exists a mixing automorphism which is not two-fold mixing. The above mentioned conjecture concerns the extent to which a mixing stationary process is determined by its two-dimensional distributions.
Reviewer: J.Woś


28D05 Measure-preserving transformations
54E52 Baire category, Baire spaces
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