Disjointness of Measure-Preserving Transformations, Minimal Self-Joinings and Category

Abstract

In the coarse topology on the group of measure-preserving transformations of a Lebesgue probability space, the class of transformations disjoint from a given ergodic transformation is a dense G_δ. The class of transformations T such that the family {Tⁱ: i ϵ ℤ} is disjoint is also a dense G_δ. As a corollary there exists an uncountable family {T_α: α ϵ A} of weakly-mixing transformations such that the family $\{ {\text{T}}_{\text{a}}^{\text{i}}:\alpha \in {\text{A,i}} \in {\Bbb Z} - \{ 0\} \}$ is disjoint.