Conditions for a generated Dynkin system to be a sigma-algebra

Statement

If $\mathcal{G}\subseteq\mathcal{P}(X)$ is $\cap$-closed then $\delta(\mathcal{G})=\sigma(\mathcal{G})$ where:

• $\delta(\mathcal{G})$ denotes the Dynkin system generated by $\mathcal{G}$ and
• $\sigma(\mathcal{G})$ denotes the $\sigma$-algebra generated by $\mathcal{G}$

Proof

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TODO: See page 32 in for help if needed

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See also

• Conditions for a Dynkin system to be a sigma-algebra