Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak approximation of an invariant measure and a low boundary of the
  entropy   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.

29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio