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e320e82 | 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 26 27 28 29 30 31 32 33 34 35 36 37 | import OAI.Combinatorics.GraphThreshold.Model
namespace OAI
noncomputable section
namespace LeanBlast.SecondKahnKalai
structure FiniteLaw (Ω : Type*) [Fintype Ω] where
weight : Ω → ℝ
nonneg : ∀ ω, 0 ≤ weight ω
total : ∑ ω, weight ω = 1
namespace FiniteLaw
def expectation {Ω : Type*} [Fintype Ω] (μ : FiniteLaw Ω) (f : Ω → ℝ) : ℝ :=
∑ ω, μ.weight ω * f ω
def prob {Ω : Type*} [Fintype Ω] (μ : FiniteLaw Ω) (P : Ω → Prop) : ℝ := by
classical
exact ∑ ω, if P ω then μ.weight ω else 0
def IsPositive {Ω : Type*} [Fintype Ω] (μ : FiniteLaw Ω) : Prop :=
∀ ω, 0 < μ.weight ω
end FiniteLaw
def IsSpread {X B : Type*} [DecidableEq X] [Fintype B]
(μ : FiniteLaw B) (A : B → Finset X) (a : ℝ) : Prop :=
∀ J : Finset X, J.Nonempty → μ.prob (fun b => J ⊆ A b) ≤ a ^ J.card
end LeanBlast.SecondKahnKalai
end
end OAI
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