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Let $\{X_\alpha\}_{\alpha \in I}$ be a collection of mutually disjoint measurable subsets of $\mathbb{R}. Show that at most countable of them has positive measure. I want to see if my proof is correct. Proof: Let $\{X_\alpha\}_{\alpha \in \Gamma \subset I}$ be the subcollection such that $m(X_...
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