  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.
