{"schema":"vela.problem-packet.v0.1","problem":994,"statement":"Let $E\\subseteq (0,1)$ be a meaurable subset with Lebesgue measure $\\lambda(E)$. Is it true that, for almost all $\\alpha$,\\[\\lim_{n\\to \\infty}\\frac{1}{n}\\sum_{1\\leq k\\leq n}1_{\\{k\\alpha \\}\\in E}=\\lambda(E)\\]for all $E$?","status":"solved","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)"}