On the cohomology of a hyperfinite action

Abstract

Let V be an ergodic automorphism of a probability space (X, , μ) and let A be a locally compact abelian group. If ƒ:X → A is a measurable function, one defines a "skew product" automorphism V_ƒ of the product space X×A by V_ƒ(x,α)=(V x,α+ƒ(x)) for every point (x,α) in X×A. In this paper we prove that V_ƒ is ergodic for "most" functions ƒ.