| import Mathlib | |
| namespace OAI | |
| open MeasureTheory ProbabilityTheory Set | |
| open scoped BigOperators ENNReal ProbabilityTheory | |
| namespace Invariant233.CouplingMixture | |
| variable {X I : Type*} [MeasurableSpace X] [Fintype I] | |
| noncomputable def diagonal (μ : Measure X) : Measure (X × X) := | |
| μ.map (fun x => (x, x)) | |
| noncomputable def mixture (μ : Measure X) (q : ℝ≥0∞) (p : I → ℝ≥0∞) | |
| (u v : I → Measure X) : Measure (X × X) := | |
| q • diagonal μ + ∑ i, p i • (u i).prod (v i) | |
| noncomputable def intervalLaw (a b : ℝ) : Measure ℝ := | |
| volume[|Ico a b] | |
| noncomputable def labelledMixture [MeasurableSpace (Option I)] (μ : Measure X) | |
| (q : ℝ≥0∞) (p : I → ℝ≥0∞) (u v : I → Measure X) : | |
| Measure (Option I × (X × X)) := | |
| q • (diagonal μ).map (fun z => (none, z)) + | |
| ∑ i, p i • ((u i).prod (v i)).map (fun z => (some i, z)) | |
| end Invariant233.CouplingMixture | |
| end OAI | |