Finitely additive measure

Summary

A finitely additive measure is a function on an algebra of sets with values in $[0, \infty]$. It is $0$ on the empty set and adds over finite disjoint unions. It is weaker than a measure, which must add over countable disjoint unions. Finitely additive measures appear in the construction of measures, in densities on the integers and in the duals of spaces of bounded functions.