Conjecture: In general a mixing transformation is not two-fold mixing (Q1063714)

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.