This theorem (or the related monotone class theorem) is an essential tool for proving many results about properties of specific σ-algebras. It capitalizes on the nature of two simpler classes of sets, namely the following. A π-system is a collection of subsets of that is closed under finitely many intersections, and A Dynkin system (or λ-system) is a collection of subsets of that contains and is closed under complement and under countable unions of disjoint subsets.
This theorem (or the related monotone class theorem) is an essential tool for proving many results about properties of specific σ-algebras It capitalizes on the nature of two simpler classes of sets namely the following A π-system is a collection of subsets of that is closed under finitely many intersections and A Dynkin system (or λ-system) is a collection of subsets of that contains and is closed under complement and under countable unions of disjoint subsets