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Let $E\subset[a,b]$ be a non-mensurable set. I want to show that:

$\exists F \in F_\sigma$ : $F\subset E$ , $\mu^*(F)=\mu_*(E)$ .

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@user32240 The set $E$ here is non-measurable. And Avril, what measure are we talking about here, the Lebesgue measure? Also, how did you define the inner measure in you class? –  Thomas E. Dec 12 '12 at 6:18

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