Monotone Class Theorem

(Theory)

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Theory
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What is Monotone class theorem?

In measure theory and probability, the monotone class theorem connects monotone classes and sigma-algebras. The theorem says that the smallest containing an algebra of sets G is precisely the smallest σ-algebra containing G. It is used as a type of transfinite induction to prove many other theorems, such as Fubini's theorem.

Technology Types

mathematical theorempropositionset familystatementtheoremtheorems in measure theorytheory

Synonyms

Monotone classMonotone class lemma

Translations

Satz über monotone Klassen (de)

Tech Info


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