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Erdős problem 501

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For every x∈Rx \in \mathbb{R} let Ax⊂RA_x \subset \mathbb{R} be a bounded set of Lebesgue outer measure <1< 1. Must there be an infinite independent set, that is an infinite X⊆RX \subseteq \mathbb{R} with x∉Ayx \notin A_y for all distinct x,y∈Xx, y \in X?

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Combinatorics47Set Theory35
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