 Premeasure

A premeasure on an algebra of sets $\mathcal{A}$ is a function ${\mu }_0:\mathcal{A}\to [0,\infty ]$ with ${\mu }_0(\varnothing )=0$ and countable additivity for every disjoint sequence whose union remains in $\mathcal{A}$. The restriction on the union is necessary because an algebra of sets need not be a sigma-algebra.