# Subsets and Sigma Algebras: Proving the Equality of Generated Sigma Algebras

a sigma algebra over $Y$.

If $B=\sigma(\mathcal{E}_{1})$ and $\mathcal{E}_{2}=\left\{ E\cap Y: \,E\in \mathcal{E}_{1}\right\}$, prove that $F=\sigma(\mathcal{E}_{2}).$

Prove that I) $F\subset \sigma(\mathcal{E}_{2}) $

II) $\sigma(\mathcal{E}_{2}) \subset F.$

Mona Vinci

39

The answer is accepted.

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