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