On the Koopman-von Neumann convergence condition of Ces\`{a}ro means in Riesz spaces

Abstract

We extend the Koopman-von Neumann convergence condition on the Ces\`{a}ro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of conditional weak mixing is given in the Riesz space setting. The results are applied to convergence in $L^1$.