adj. (of a set function, S, defined on a class of sets) having the property that, for any countable pairwise disjoint family of sets {A_n}_n∈N in the class, S(∪_n∈N A_n) = Σ_n∈N S(A_n).
whenever the union lies in the given class. For example, by definition, a measure is countably additive on its sigma-algebra. Compare additive.