Sigma-ring
σ-ring

Thus, what is missing for a pre-measure to be a measure is that it is not necessarily defined on a sigma-algebra (or a sigma-ring).

As a corollary, if G is a ring of sets, then the smallest monotone class containing it coincides with the sigma-ring of G.

In mathematics, a nonempty collection of sets is called a σ-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation: