Let X be a set and S a collection of subsets of X. A set function μ:S->[0, ∞] is said to possess finite monotonicity provided that, whenever a set E element S is covered by a finite collection {E_k}_(k = 1)^n of sets in S, μ(E)<= sum_(k = 1)^n μ(E_k). A set function possessing finite monotonicity is said to be finitely monotone. Note that a set function μ which is countably monotone is necessarily finitely monotone provided that ∅ element S and μ(∅) = 0, where ∅ is the empty set.

countable monotonicity | cover | monotone | set function