Uniform continuity of entropy on the regular points endowed with $f$-bar.

Given a sequence $x=x_0x_1\ldots$ which is frequency-typical for a finite-valued stationary stochastic process, write $h(x)$ for the entropy of that process. We prove that the function $h$ is uniformly continuous when one endows the set of all frequency-typical sequences with the $f$-bar (pseudo)distance. We also give an alternative proof of the Abramov formula for entropy of the induced transformation.