熵率关于$\bar f$ -伪度量的一致连续性
Uniform continuity of entropy rate with respect to the $\bar f$-pseudometric
摘要：
假设序列$x=x_0x_1\ldots$对于有限值平稳随机过程$\textbf X$是频率典型的。证明了当赋予所有频率典型序列的集合以$\bar f$伪度量时，关联到$x$的$\textbf X$的熵率$\bar H(\textbf X)$的函数是一致连续的.因此，对于$\bar d$伪度量，我们得到了相同的结果。我们还给出了另一种证明的阿布拉莫夫公式的诱导保测变换的Kolmogorov-Sinai熵。
英文摘要：
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.
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