Difference between revisions of "Conditions for a Dynkin system to be a sigma-algebra"
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(Created page with "==Statement== A Dynkin system {{M|\mathcal{D} }} is a algebra}} ''if and only if''<ref name="MIM">Measures, Integrals and Martingales</ref> it is...") |
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| − | == | + | 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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<references group="Note"/> | <references group="Note"/> | ||
| + | ==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== | ||
<references/> | <references/> | ||
{{Theorem Of|Measure Theory}} | {{Theorem Of|Measure Theory}} | ||
Latest revision as of 22:56, 2 August 2015
This page is intended to list different conditions for a Dynkin system (also called a [ilmath]d[/ilmath]-system) to be a [ilmath]\sigma[/ilmath]-algebra
Conditions
- A Dynkin system, [ilmath]\mathcal{D} [/ilmath] is a [ilmath]\sigma[/ilmath]-algebra if and only if it is [ilmath]\cap[/ilmath]-closed (which is to say it is also a [ilmath]p[/ilmath]-system)[1][2]
See also
References
