Nonstandard analysis of the behavior of ergodic means of dynamical systems on very big finite probability spaces

E. I. Gordon, L. Yu. Glebsky, C. W. Henson

The trivial proof of the ergodic theorem for a finite set $Y$ and a permutation $T:Y\to Y$ shows that for an arbitrary function $f:Y\to \mathbb{R}$ the sequence of ergodic means $A…