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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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Problem row
sha256:7577f50e95ad4caae796e9539e08f8bfbd3db50c986268f5fcf2a6fed2f245e2
Metadata
sha256:dff73c36e494854297047cb4c22f91cde96d4003548bb47a2e41f7fdf6eb8682
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:7a34ff54b8b2cceb5f79a292be1e8f51287002ac0618796805ff58266d9f402c
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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