Lipschitz functions and the prevalence of strict ergodicity for continuous-time flows

Abstract

In a recent paper, R. Jewett has shown that every weakly mixing transformation in a separable probability space can be considered, up to a measure algebra isomorphism, as a strictly ergodic homeomorphism in some compact metric set. The present paper provides the analogous result for continuous-time flows: neglecting some measure algebra isomorphism, weakly mixing flows in separable probability spaces can be considered as shift flows on strictly ergodic subsets of a compact metric space made out of certain Lipschitz functions. As a preparatory tool, we use the Ambrose-Kakutani theorem in order to obtain flows built under functions. A combination of Jewett's devices and new ideas is then applied in order to obtain the desired embedding.

Research done during a visit at the Ohio State University, Columbus, Ohio, U.S.A., 1969/70.