Shearer's inequality
Shearer's inequality is an inequality in information theory relating the entropy a set of variables to the entropies of a collection of subsets. It is named for mathematician James Shearer.
Concretely, it states that if X1, ..., Xd are random variables and S1, ..., Sn are subsets of such that every integer between 1 and d lies in at least r of these subsets, then
where is entropy and is the Cartesian product of random variables with indices j in.
