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Reference.org
Monotone class theorem
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<p>In <a href="/facts/Measure_(mathematics)/yCq7zlI4">measure theory</a> and <a href="/facts/Probability_theory/mFBn51rE">probability</a>, the monotone class theorem connects monotone classes and <a href="/facts/Sigma-algebra/8LJINLNc">𝜎-algebras</a>. The theorem says that the smallest monotone class containing an <a href="/facts/Field_of_sets/4E3vQl4f">algebra of sets</a> G {\displaystyle G} is precisely the smallest <a href="/facts/Sigma-algebra/8LJINLNc">𝜎-algebra</a> containing G . {\displaystyle G.} It is used as a type of <a href="/facts/Transfinite_induction/XlolgTDl">transfinite induction</a> to prove many other theorems, such as <a href="/facts/Fubini%2527s_theorem/q4lhtS3s">Fubini's theorem</a>. </p>