Finitely Additive Probability Measure

A finitely additive probability measure on an algebra of sets on a set is a set function with , , and

for disjoint sets . This gives finite additivity for any finite family of pairwise disjoint sets. Countable additivity is not required (Juschenko 2015, p. 28).

Every probability measure is finitely additive on its sigma-algebra, but the converse need not hold. For subsets of a finite set , normalized counting measure gives when is nonempty. In the definition of an amenable group, the finitely additive probability measure is defined on all subsets of the group.