Shannon熵和拓扑熵的Shearer不等式和下确界规则
Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy
摘要：
我们回顾了Shannon熵的次可加性性质，特别地，从Shearer不等式导出了顺从群作用的“下确界规则”。我们简要讨论了“下确界公式”对其他基团作用的适用性。然后，我们传递到覆盖的拓扑熵。证明了不交覆盖的Shearer不等式，并给出了反例.我们还证明了，对于顺从群的作用，“下确界公式”的所有开覆盖上的上确界给出了正确的拓扑熵值。
英文摘要：
We review subbadditivity properties of Shannon entropy, in particular, from the Shearer's inequality we derive the "infimum rule" for actions of amenable groups. We briefly discuss applicability of the "infimum formula" to actions of other groups. Then we pass to topological entropy of a cover. We prove Shearer's inequality for disjoint covers and give counterexamples otherwise. We also prove that, for actions of amenable groups, the supremum over all open covers of the "infimum fomula" gives correct value of topological entropy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
