{"articles":{"thm-3.4@measure-theory":{"content":"<p>Intersection of sigma algebras on X is sigma algebra.</p><p>For system G there is a coarsest σ-algebra containing G.</p><p>(i) Arbitrary intersection of σ-algerbras is σ-algebra.</p><p>(ii) For every system of subsets \\(\\mathcal{G}\\) of \\(X\\) there is a smallest σ-algebra containing \\(\\mathcal{G}\\).</p><p>G is called generator, σ(G) is sigma algebra generated by G.</p>","names":[[["Theorem",""]]]}},"style":"Statement"}