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) |
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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'' | + | <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 D⊆P(X) is a Dynkin system[1] if:
- X∈D
- For any D∈D we have Dc∈D
- For any (Dn)∞n=1⊆D is a sequence of pairwise disjoint sets we have ∪⋅∞n=1Dn∈D