@inbook{ae9f89ddaaf64cf09d608b808ba45c2a,
title = "Shearer{\textquoteright}s inequality and infimum rule for shannon entropy and topological entropy",
abstract = "We review subbadditivity properties of Shannon entropy, in particular, from the Shearer{\textquoteright}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{\textquoteright}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.",
keywords = "Infimum rule, Shannon entropy, Shearer{\textquoteright}s inequality, Strong subadditivity, Subadditivity, Topological entropy",
author = "Tomasz Downarowicz and Bartosz Frej and Romagnoli, {Pierre Paul}",
note = "Publisher Copyright: {\textcopyright} 2016 American Mathematical Society.",
year = "2016",
doi = "10.1090/conm/669/13423",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "63--75",
booktitle = "Contemporary Mathematics",
address = "United States",
}