| import Mathlib | |
| namespace OAI | |
| noncomputable section | |
| namespace Problem310 | |
| def dyadicPoint (n : ℕ) : ℝ := | |
| (2 : ℝ)⁻¹ ^ n | |
| theorem dyadic_affine_avoidance : | |
| ∀ η : ℝ, 0 < η → η < 1 → ∃ E : Set ℝ, | |
| E ⊆ Set.Icc (0 : ℝ) 1 ∧ IsCompact E ∧ | |
| MeasureTheory.volume E > ENNReal.ofReal (1 - η) ∧ | |
| ∀ x s : ℝ, s ≠ 0 → ∃ n : ℕ, 1 ≤ n ∧ | |
| x + s * dyadicPoint n ∉ E := by | |
| sorry | |
| end Problem310 | |
| end | |
| end OAI | |