Type of a set function
Also known as finitely additive set function
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\mu(A \cup B) = \mu(A) + \mu(B), \forall A, B: A \cap B = \emptyset 1 identifiers linking additive set function across the web's reference databases
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In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets equals the sum of its values on the sets. Therefore, an additive set function is also called a finitely additive set function. However, a finitely additive set function might not have the additivity property for a union of an infinite number of sets. A σ-additive set function is a function that has the additivity property even for countably infinite many sets, that is,