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f61e547 | 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 OAI.Probability.FreeIsing.Estimates.UniformSampler
import OAI.Probability.FreeIsing.Factors.Transfer
namespace OAI
noncomputable section
open MeasureTheory
namespace Problem367
theorem isFactorOfIID_of_standardBorelNoise {d : ℕ} {theta : ℝ}
{A : Type*} [MeasurableSpace A] [Nonempty A] [StandardBorelSpace A]
(ν : Measure A) [IsProbabilityMeasure ν]
(H : (TreeVertex d → A) → (TreeVertex d → IsingSpin))
(hH : Measurable H)
(hlaw : HasFreeIsingLaw theta
(Measure.map H (Measure.infinitePi (fun _ : TreeVertex d => ν))))
(heq : ∀ g : TreeAut d,
∀ᵐ W ∂Measure.infinitePi (fun _ : TreeVertex d => ν),
H (relabel g W) = relabel g (H W)) :
IsFactorOfIID d theta := by
obtain ⟨ξ, hξ, hν⟩ := exists_uniform01_sampler ν
exact isFactorOfIID_of_product_sampler ν ξ hξ hν H hH hlaw heq
end Problem367
end
end OAI
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