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 $x, y \in X$?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

1True ↔2  ∀ (A : ℝ → Set ℝ),3    (∀ (x : ℝ), Bornology.IsBounded (A x)) →4      (∀ (x : ℝ), MeasureTheory.volume.toOuterMeasure (A x) < 1) → ∃ X, X.Infinite ∧ X.Pairwise fun x y => x ∉ A y

Reported activity

Reported by these sources. Not reviewed here.

• AI collaborating with humans

  Erdős AI contributions wiki · 29 May-1 Jun, 2026

  Machine

  GPT-5.5 Pro

  People

  Sungchul Lee

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• argument

  VibeMathed

  Machine

  Sol, Claude

  People

  Elliot Glazer

  Reported outcome

  resolved

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