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I am having difficulty understanding the proof of that theorem:
First the definition:
then the theorem i am having difficulty understanding the proof of:
Now, I do understand that the class $\varepsilon$ exists in the first place because $C \subset \varepsilon$ by hypothesis, and yes, it is a sigma-algebra by (a). But what we want to prove is: for any element $A$ in the Borel sets, $h^{-1}(A) \in \Sigma$, so I am missing a step here ...
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$\begingroup$$\mathcal{E}$ is a $\sigma$-algebra containing $\mathcal{C}$, so it contains the $\sigma$-algebra $\mathcal{B}$ generated by $\mathcal{C}$.
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