Shearer's inequality and infimum rule for Shannon entropy and topological entropy
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Publication:2827676
DOI10.1090/CONM/669/13423zbMATH Open1376.37010arXiv1502.07459OpenAlexW1535994060MaRDI QIDQ2827676
Author name not available (Why is that?)
Publication date: 20 October 2016
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1502.07459
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