Subsets and Sigma Algebras: Proving the Equality of Generated Sigma Algebras
Let $X$ a set and $Y$ a subset of $X$. Let $B$ a sigma algebra over $X$ and $F=\left\{ E\cap Y:\,E\in B\right\}$
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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