| 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 | |