Given a topological dynamical system $(X,T)$, we study properties of the mean orbital pseudo-metric $\bar E$ defined by \[ \bar E(x,y)= \limsup_{n\to\infty } \min_{\sigma\in S_n}\frac{1}{n}\sum_{k=0}^{n-1}d(T^k(x),T^{\sigma(k)}(y)), \] where $x,y\in X$ and $S_n$ is permutation group $\{0,1,\ldots,n-1\}$. Let $\hat\omega_T(x)$ denote set measures quasi-generated point $x\in X$. We show that map ...
