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b317718 | 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 | import OAI.Probability.InvariantIsing.Fields.NoiseReplicaPairData
import OAI.Probability.IsingPerceptron.SamplingIndependent
namespace OAI
/-! The measurable labeled two-path observable in the original forest coordinates. -/
noncomputable section
open MeasureTheory ProbabilityTheory IsingPerceptron
namespace InvariantIsing
def coordinatePairData {A : Type} (n : ℕ)
(p : (ForestVertex n → A) × (ℕ → LabeledLeaf n)) : ℕ × (Fin n → A × A) :=
(labeledCommonDepth n (p.2 0) (p.2 1),
fun i => (p.1 (edgeAt n (p.2 0) i),p.1 (edgeAt n (p.2 1) i)))
lemma measurable_coordinatePairData {A : Type} [MeasurableSpace A] (n : ℕ) :
Measurable (coordinatePairData (A := A) n) := by
have hE : Measurable (fun p : (ForestVertex n → A) × LabeledLeaf n =>
fun i => p.1 (edgeAt n p.2 i)) := by
apply measurable_from_prod_countable_left
intro α
exact Measurable.of_eval fun i => measurable_pi_apply (edgeAt n α i)
have hp (j : ℕ) : Measurable (fun p : (ForestVertex n → A) × (ℕ → LabeledLeaf n) =>
(p.1,p.2 j)) := measurable_fst.prodMk ((measurable_pi_apply j).comp measurable_snd)
have hd : Measurable (fun p : (ForestVertex n → A) × (ℕ → LabeledLeaf n) =>
(p.2 0,p.2 1)) := ((measurable_pi_apply 0).comp measurable_snd).prodMk
((measurable_pi_apply 1).comp measurable_snd)
exact ((measurable_of_countable (fun q : LabeledLeaf n × LabeledLeaf n =>
labeledCommonDepth n q.1 q.2)).comp hd).prodMk (Measurable.of_eval fun i =>
((measurable_pi_apply i).comp (hE.comp (hp 0))).prodMk
((measurable_pi_apply i).comp (hE.comp (hp 1))))
end InvariantIsing
end
end OAI
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