Monotone class theorem: Difference between revisions

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In [[Measure (mathematics)|measure theory]] and [[Probability theory|probability]], the '''monotone class theorem''' connects monotone classes and [[sigma-algebra]]s. The theorem says that the smallest [[#Definition of a monotone class|monotone class]] containing an [[Field of sets|algebra of sets]] <math>G</math> is precisely the smallest [[Sigma-algebra|{{sigma}}-algebra]] containing&nbsp;<math>G.</math> It is used as a type of [[transfinite induction]] to prove many other theorems, such as [[Fubini's theorem]].

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== See also ==

* {{annotated link|π-λ theorem|{{pi}}-{{lambda}} theorem}}

* {{annotated link|Pi-system|{{pi}}-system}}

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== Citations ==

{{reflist|group=note}}

{{reflist}}

== References ==

* {{Durrett Probability Theory and Examples 5th Edition}} <!-- {{sfn|Durrett|2019|p=}} -->

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[[Category:Set families]]