File size: 995 Bytes
a89d282 | 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 | import OAI.Probability.InvariantIsing.Pressure.RandomOrbitLaw
namespace OAI
/-! Transporting deterministic orbit bounds through the joint conditional law. -/
noncomputable section
open MeasureTheory ProbabilityTheory Set
namespace InvariantIsing
lemma ConditionalFieldOrbitLaw.ae_property {Ω : Type*} [MeasurableSpace Ω] {N : ℕ}
(hN : 0 < N) (P : Measure Ω) (d : Ω → FieldSpectralData N) (Y : Ω → ℝ)
(hd : Measurable d) (hY : Measurable Y)
(H : Measure (Orthogonal N)) [SFinite H]
(hlaw : ConditionalFieldOrbitLaw P d Y H)
(Q : FieldSpectralData N × ℝ → Prop) (hQ : MeasurableSet {z | Q z})
(hbound : ∀ data U, Q (data,dataPhysicalPressure data U)) :
∀ᵐ ω ∂P, Q (d ω,Y ω) := by
apply ae_of_ae_map (hd.prodMk hY).aemeasurable
rw [hlaw]
apply (ae_map_iff (measurable_fst.prodMk (measurable_dataPhysicalPressure hN)).aemeasurable hQ).mpr
exact Filter.Eventually.of_forall fun z => hbound z.1 z.2
end InvariantIsing
end
end OAI
|