openAI-math-dataset / lean /OAI /Probability /CriticalPercolation /ProductMeasure /ExposureLawSupport.lean
| 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 | |