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dae740b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | 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
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