  Assume that a sequence $x=x_0x_1\ldots$ is frequency-typical for a
finite-valued stationary stochastic process $\textbf X$. We prove that the
function associating to $x$ the entropy-rate $\bar H(\textbf X)$ of $\textbf X$
is uniformly continuous when one endows the set of all frequency-typical
sequences with the $\bar f$ pseudometric. As a consequence, we obtain the same
result for the $\bar d$ pseudometric. We also give an alternative proof of the
Abramov formula for the Kolmogorov-Sinai entropy of the induced
measure-preserving transformation.
