Wen HUANG, Run Ju WEI, Tao YU, Xiao Min ZHOU
In this paper we introduce two metrics: the max metric dn, q and the mean metric dn, q. We give an equivalent characterization of rigid measure preserving systems by the two metrics. It turns out that an invariant measure μ on a topological dynamical system (X, T) has bounded complexity with respect to dn, q if and only if μ has bounded complexity with respect to dn, q if and only if (X, BX, μ, T) is rigid. We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system (resp. the topological entropy of a topological dynamical system) by the two metrics dn, q and dn, q.