A set function μ possesses countable additivity if, given any countable disjoint collection of sets {E_k}_(k = 1)^n on which μ is defined, μ( union _(k = 1)^∞ E_k) = sum_(k = 1)^∞ μ(E_k). A function having countable additivity is said to be countably additive. Countably additive functions are countably subadditive by definition. Moreover, provided that μ(∅) = 0 where ∅ is the empty set, every countably additive function μ is necessarily finitely additive.

countable additivity probability axiom | countable subadditivity | disjoint union | finite additivity | set function