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9eeb9c7 | 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
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
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