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a2ee19a | 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 32 33 34 35 36 37 38 39 40 41 | import OAI.Probability.PosteriorReplicas.Measures.BaseDisintegration
namespace OAI
open MeasureTheory ProbabilityTheory Set
open scoped ENNReal NNReal RealInnerProductSpace
noncomputable section
namespace PosteriorReplicas
@[fun_prop] lemma measurable_basePoint_comp {X : Type*} [MeasurableSpace X]
{d k : ℕ} (base : BaseLaw) {A : X → Rows d k} {y : X → Labels k} {x : X → Vec d}
(hA : Measurable A) (hy : Measurable y) (hx : Measurable x) :
Measurable (fun z => basePoint base (A z) (y z) (x z)) := by
have h := (measurable_basePoint (d := d) (k := k) base).comp ((hA.prodMk hy).prodMk hx)
exact h
@[fun_prop] lemma measurable_baseDensity_comp {X : Type*} [MeasurableSpace X]
{d k : ℕ} (base : BaseLaw) {A : X → Rows d k} {y : X → Labels k}
(hA : Measurable A) (hy : Measurable y) :
Measurable (fun z => baseDensity base (A z) (y z)) := by
have h := (measurable_baseDensity (d := d) (k := k) base).comp (hA.prodMk hy)
exact h
@[fun_prop] lemma measurable_kernelComponent_comp {X : Type*} [MeasurableSpace X]
{d k : ℕ} {A : X → Rows d k} {x : X → Vec d}
(hA : Measurable A) (hx : Measurable x) :
Measurable (fun z => kernelComponent (A z) (x z)) := by
have h := (measurable_kernelComponent (d := d) (k := k)).comp (hA.prodMk hx)
exact h
@[fun_prop] lemma measurable_labels_comp {X : Type*} [MeasurableSpace X]
{d k : ℕ} {A : X → Rows d k} {x : X → Vec d}
(hA : Measurable A) (hx : Measurable x) :
Measurable (fun z => labels (A z) (x z)) := by
have h := (measurable_labels (d := d) (k := k)).comp (hA.prodMk hx)
exact h
end PosteriorReplicas
end
end OAI
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