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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 32 | import OAI.Analysis.IrrationalRotation.Model.CircleConditionalLabels
import OAI.Analysis.IrrationalRotation.Couplings.CircleConditionalProbabilities
namespace OAI
noncomputable section
namespace Invariant233.CircleCoupling
theorem conditionalLabelLaws {θ : ℝ} {p : CircleParameterData}
(hp : CircleParameterLaws θ p) (j : ℕ)
(hr : ∀ i, 0 < MixedRadix.radices p.q i) : ConditionalLabelLaws p j hr where
probability := law_isProbabilityMeasure hp j
endpoint_measurable := measurable_point hp hr
independent := iCondIndepFun_labels_point hp j hr
finite_posterior := condExp_labels_point hp j hr
top_probability := fun _ hs _ hi which => ae_top_conditional_probability hp j hr hs hi which
bottom_probability := fun _ hs _ hi which => ae_bottom_conditional_probability hp j hr hs hi which
top_forcing := fun _ hs _ hi which => ae_top_forces hp j hr hs hi which
bottom_forcing := fun _ hs _ hi which => ae_bottom_forces hp j hr hs hi which
theorem exists_conditionalLabelLaws {θ : ℝ} {p : CircleParameterData}
(hp : CircleParameterLaws θ p) (j : ℕ) :
∃ hr : ∀ i, 0 < MixedRadix.radices p.q i, ConditionalLabelLaws p j hr :=
⟨MixedRadix.radices_pos hp.q_pos hp.frequency_increasing hp.frequency_divisible,
conditionalLabelLaws hp j _⟩
end Invariant233.CircleCoupling
end
end OAI
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