Weak approximation of an invariant measure and a low boundary of the entropy

Abstract

For a measurable map $T$ and a sequence of $T$-invariant probability measures ${\mu }_n$ that converges in some sense to a $T$-invariant probability measure $\mu$, an estimate from below for the Kolmogorov--Sinai entropy of $T$ with respect to $\mu$ is suggested in terms of the entropies of $T$ with respect to ${\mu }_1$, ${\mu }_2$, \dots.

3 pages