theorem
BooleanFourier.isBooleanValued_hasBoundedRange
{n : ℕ}
{f : (Fin n → Bool) → ℝ}
(hf : IsBooleanValued f)
:
theorem
BooleanFourier.majority_is_stablest_boolean
(ρ : ℝ)
(hρ₀ : 0 ≤ ρ)
(hρ₁ : ρ < 1)
(ε : ℝ)
(hε : 0 < ε)
:
∃ δ > 0,
∀ (n : ℕ) (f : (Fin n → Bool) → ℝ),
IsBooleanValued f → maxInfluence f ≤ δ → noiseStability ρ f ≤ halfspaceNoiseStability ρ (boolExpectation f) + ε