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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 | import Mathlib
import OAI.Probability.CriticalPercolation.ProductMeasure.Density
namespace OAI
section
section
open scoped BigOperators
open Set MeasureTheory ProbabilityTheory
namespace CriticalPercolation.FiniteProduct
variable {E B : Type*} [Fintype E] [Fintype B]
lemma continuous_expect_weights (f : (E → B) → ℝ) :
Continuous (fun w : E → B → ℝ => expect w f) := by
classical
unfold expect density
apply continuous_finsetSum
intro ω _
apply Continuous.mul _ continuous_const
apply continuous_finsetProd
intro e _
exact (continuous_apply (ω e)).comp (continuous_apply e)
end CriticalPercolation.FiniteProduct
end
end
end OAI
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