Uniform continuity of entropy rate with respect to the $\\bar\n f$-pseudometric Article Swipe
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Tomasz Downarowicz
,
Dominik Kwietniak
,
Martha Łącka
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2007.14496
· OA: W4287704379
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2007.14496
· OA: W4287704379
Assume that a sequence $x=x_0x_1\\ldots$ is frequency-typical for a\nfinite-valued stationary stochastic process $\\textbf X$. We prove that the\nfunction associating to $x$ the entropy-rate $\\bar H(\\textbf X)$ of $\\textbf X$\nis uniformly continuous when one endows the set of all frequency-typical\nsequences with the $\\bar f$ pseudometric. As a consequence, we obtain the same\nresult for the $\\bar d$ pseudometric. We also give an alternative proof of the\nAbramov formula for the Kolmogorov-Sinai entropy of the induced\nmeasure-preserving transformation.\n
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