Strictly ergodic models for non-invertible transformations
A continuous transformation of a compact metric space Y is said to be strictly ergodic, if there is a unique Borel probability measure \(\nu\), fixed by the action, and \(\nu (U)>0\) for every non-empty open set \(U\subset Y\). In 1969 R. Jewett proved that weakly mixing invertible transformation on a Lebesgue space is measure isomorphic to a strictly ergodic transformation. In 1983 B. Weiss extended this result to any ergodic free action of an elementary amenable group. Using Weiss' method, the author obtains a similar result in the case of non-invertible transformation.
scientific article; zbMATH DE number 4142373