Shearer’s inequality and infimum rule for Shannon entropy and topological entropy
Shearer’s inequality and infimum rule for Shannon entropy and topological entropy
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 …