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

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. This result is obtained under the assumption that some generating partition has finite entropy. By an explicite example it is shown that, in general, this assumption cannot be removed.

arXiv comment7 pages