View source for Conditions for a Dynkin system to be a sigma-algebra

This page is intended to list different conditions for a [[Dynkin system]] (also called a {{M|d}}-system) to be a [[Sigma-algebra|{{sigma|algebra}}]]
==Conditions==
* [[A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections|A Dynkin system, {{M|\mathcal{D} }} is a {{sigma|algebra}} ''if and only if'' it is {{M|\cap}}-closed (which is to say it is also a {{M|p}}-system)]]<ref name="MIM">Measures, Integrals and Martingales</ref><ref name="PAS">Probability and Stochastics - Erhan Cinlar</ref>
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==See also==
* [[Conditions for a generated Dynkin system to be a sigma-algebra|Conditions for a generated Dynkin system to be a {{sigma|algebra}}]]

==References==
<references/>
{{Theorem Of|Measure Theory}}