Conditions for a generated Dynkin system to be a sigma-algebra
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Contents
Statement
If [ilmath]\mathcal{G}\subseteq\mathcal{P}(X)[/ilmath] is [ilmath]\cap[/ilmath]-closed then[1] [ilmath]\delta(\mathcal{G})=\sigma(\mathcal{G})[/ilmath] where:
- [ilmath]\delta(\mathcal{G})[/ilmath] denotes the Dynkin system generated by [ilmath]\mathcal{G} [/ilmath] and
- [ilmath]\sigma(\mathcal{G})[/ilmath] denotes the [ilmath]\sigma[/ilmath]-algebra generated by [ilmath]\mathcal{G} [/ilmath]
Proof
TODO: See page 32 in[1] for help if needed
See also
References
