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f205175 | 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 | import Mathlib
import OAI.Probability.CriticalPercolation.ProductMeasure.ExposureLaw
namespace OAI
section
section
open Set MeasureTheory ProbabilityTheory
open Set
open scoped BigOperators
open scoped Classical
namespace CriticalPercolation.FiniteProduct
open scoped Classical
variable {E A : Type*} [Fintype E]
lemma exposureLaw_support (w : E → A → ℝ) (D : Set E) (σ ω : E → A)
(hω : density (exposureLaw w D σ) ω ≠ 0) : ∀ e ∈ D, ω e = σ e := by
intro e he
by_contra hb
apply hω
unfold density
exact Finset.prod_eq_zero (Finset.mem_univ e) (by simp [exposureLaw,he,hb])
end CriticalPercolation.FiniteProduct
end
end
end OAI
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