A set function μ is said to possess countable subadditivity 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 possessing countable subadditivity is said to be countably subadditive. Any countably subadditive function μ is also finitely subadditive presuming that μ(∅) = 0 where ∅ is the empty set.

disjoint union | finite subadditivity | set function