Ergodic Theory and Dynamical Systems

Measurable distal and topological distal systems

a1 Hebrew University, Jerusalem, Israel (e-mail:


In this paper we prove that any ergodic measurably distal system can be realized as a minimal topologically distal system with an invariant Borel measure of full support. The proof depends upon a theorem stating that every measurable function from a measurable system with its base space being a compact metric space to a connected compact group is cohomologous to a continuous function.

(Received June 5 1997)
(Revised August 29 1997)