{"schema":"vela.problem-packet.v0.1","problem":501,"statement":"For every $x\\in\\mathbb{R}$ let $A_x\\subset \\mathbb{R}$ be a bounded set with outer measure $<1$. Must there exist an infinite independent set, that is, some infinite $X\\subseteq \\mathbb{R}$ such that $x\\not\\in A_y$ for all $x\\neq y\\in X$?If the sets $A_x$ are closed and have measure $<1$, then must there exist an independent set of size $3$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}