Monotone class theorem: Difference between revisions

Revision as of 18:21, 8 August 2023

Revision as of 12:02, 7 September 2023

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==Results and applications==

As a corollary, if <math>G</math> is a [[ring of sets]] of sets, then the smallest monotone class containing it coincides with the [[Sigma-ring|{{sigma}}-ring]] of <math>G.</math>

By invoking this theorem, one can use monotone classes to help verify that a certain collection of subsets is a [[Sigma-algebra|{{sigma}}-algebra]].