A nonempty collection of subsets of a fixed universe closed under complements and finite unions, hence also finite intersections. It generates a sigma-algebra by allowing countable set operations. A countable generating algebra provides one simultaneous family of test indicators for measure-theoretic arguments.
A countable algebra of sets generating the intended sigma-algebra. Standard Borel spaces admit such algebras by taking finite Boolean combinations from a countable topological base. Finite linear combinations of its indicators are dense in for every Borel probability measure, by the Monotone class theorem. Countability permits a common full-measure convergence set for all test indicators.
