论文标题
相对于$ \ bar f $ -peudricrymementricry的熵率均匀连续性
Uniform continuity of entropy rate with respect to the $\bar f$-pseudometric
论文作者
论文摘要
假设一个序列$ x = x_0x_1 \ ldots $对于有限价值的固定随机过程$ \ textbf x $是频率类型。我们证明，与$ x $相关的函数$ \ textbf x $的熵率$ \ bar h（\ textbf x）$是均匀连续的。结果，我们获得了$ \ bar d $ pseudogetric的相同结果。我们还为诱导的量子标准转换的Kolmogorov-Sinai熵提供了Abramov公式的替代证明。
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.
