Additive (or Finitely Additive) Set Functions
Let be a function defined on an algebra of sets with values in (see the extended real number line). The function is called additive, or finitely additive, if, whenever A and B are disjoint sets in one has
(A consequence of this is that an additive function cannot take both −∞ and +∞ as values, for the expression ∞ − ∞ is undefined.)
One can prove by mathematical induction that an additive function satisfies
for any disjoint sets in .
Read more about this topic: Sigma Additivity
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