  The article considers generic extensions of measure-preserving actions. We
prove that the P-entropy of the generic extensions with finite P-entropy is
infinite. This is exploited to obtain the result by Austin, Glasner, Thouvenot,
and Weiss that the generic extension of an deterministic action is not
isomorphic to it. We show also that generic cocycles are recurrent; as well as
typical extensions preserve the singularity of the spectrum, partial rigidity,
mildly mixing, and mixing. At the same time, the lifting of some algebraic
properties under the generic extension may depend on the statistical properties
of the base. The typical measurable families of automorphisms are considered as
well. The dynamic behavior of such families is a bit unusual. It is
characterized by a combination of the dynamic conformism with the dynamic
individualism of the representatives of the generic family.

Dynamical Systems