Let ($X, Beta, mu$) be a measure space with the $sigma$-algebra $Beta$ and the probability measure $mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $mu(T^{-1}E) = mu(E)$ for $E in B$. It is said to be ergodic if $mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set Eulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n o infty}(1/N)sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/mu(X)) int_X f(x)dmu(x)$. In the special case when f is the characteristic function $chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N o infty} frac{$mid${n : T^n x in E, 0 leq n <N}$mid$}{N} = mu(E) $$</TEX> for almost all $x in X$ where $$mid$cdot$mid$$</TEX> denotes cardinality of a set. For the details, see [8], [10].