Deterministic functions on amenable semigroups and a generalization of the Kamae-Weiss theorem on normality preservation

Vitaly Bergelson, Tomasz Downarowicz, Joseph Vandehey

A classical Kamae-Weiss theorem states that an increasing sequence $(n_i{)}_{i\in \mathbb{N}}$ of positive lower density is \emph{normality preserving}, i.e. has the property that for…