
generator of sigmafield
Hallo,
I have an enlarged sigmafield $\displaystyle \sigma(\mathcal{F}\vee \sigma(X))$ (that is the smallest sigmafield containing the sigmafields $\displaystyle \mathcal{F} \text{ and }\sigma(X)$?
How does the generator of this (enlarged) sigmafield look like?
Is this sigmafield generated by sets of the form $\displaystyle \{A \cap B: A \in\mathcal{F},B \in \sigma(X)\}$,
i.e.
$\displaystyle \sigma(\{A \cap B: A \in\mathcal{F},B \in \sigma(X)\})=\sigma(\mathcal{F}\vee \sigma(X))$?
Thanks in advance