Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy
Dynamical Systems
2015-02-27 v1
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.
Keywords
Cite
@article{arxiv.1502.07459,
title = {Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy},
author = {Tomasz Downarowicz and Bartosz Frej and Pierre-Paul Romagnoli},
journal= {arXiv preprint arXiv:1502.07459},
year = {2015}
}
Comments
12 pages