Erdős problem 501 · problems.science

For every $x \in \mathbb{R}$ let $A_x \subset \mathbb{R}$ be a bounded set of Lebesgue outer measure $< 1$ . Must there be an infinite independent set, that is an infinite $X \subseteq \mathbb{R}$ with $x \notin A_y$ for all distinct $x, y \in X$ ?

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14 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

501.lean

Retained formal statement3 of 13

Two reals form an independent set for the empty family A _ = ∅: neither 0 nor 1 belongs to ∅, so both conditions of pair_independent_iff hold.

FormalConjectures/ErdosProblems/501.leanErdos501.erdos_501.tests.pair_independent_empty1 lineExact file

1{0, 1}.Pairwise fun x y => x ∉ (fun x => ∅) y

TestStatement only, no proof

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