Difference between revisions of "Dynkin system/Definition 1"

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m (Alec moved page Dynkin system/Definiton 1 to Dynkin system/Definition 1 without leaving a redirect: Another typo)
m (Updated reference to use templates)
 
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<noinclude>{{Extra Maths}}</noinclude>Given a set {{M|X}} and a family of subsets of {{M|X}}, which we shall denote {{M|\mathcal{D}\subseteq\mathcal{P}(X)}} is a ''Dynkin system''<ref name="MIM">Rene L. Schilling - Measures, Integrals and Martingales</ref> if:
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<noinclude>{{Extra Maths}}</noinclude>Given a set {{M|X}} and a family of subsets of {{M|X}}, which we shall denote {{M|\mathcal{D}\subseteq\mathcal{P}(X)}} is a ''Dynkin system''{{rMIAMRLS}} if:
 
* {{M|X\in\mathcal{D} }}
 
* {{M|X\in\mathcal{D} }}
 
* For any {{M|D\in\mathcal{D} }} we have {{M|D^c\in\mathcal{D} }}
 
* For any {{M|D\in\mathcal{D} }} we have {{M|D^c\in\mathcal{D} }}

Latest revision as of 01:52, 19 March 2016

Given a set X and a family of subsets of X, which we shall denote DP(X) is a Dynkin system[1] if:

  • XD
  • For any DD we have DcD
  • For any (Dn)n=1D is a sequence of pairwise disjoint sets we have n=1DnD

References

  1. Jump up Measures, Integrals and Martingales - René L. Schilling