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