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Let $R$ be the smallest $\sigma$-algebra containing all compact sets in $\mathbb R^n$. I know that based on definition the minimal $\sigma$-algebra containing the closed (or open) sets is the Borel $\sigma$-algebra. But how can I prove that $R$ is actually the Borel $\sigma$-algebra?

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    In the second sentence, do you want to say _open_ sets?2012-09-05
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    I think the question should say "_the_ Borel $\sigma$-algebra"2012-09-05
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    @Dylan Moreland that is another definition of it2012-09-05
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    @Ana Well, that's what the exercise shows :) But what is written seems like a tautology.2012-09-05

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