| import OAI.Probability.FreeIsing.Estimates.ProjectiveExtension | |
| namespace OAI | |
| noncomputable section | |
| open MeasureTheory ProbabilityTheory | |
| open scoped NNReal | |
| namespace Problem367.BrownianExistence | |
| theorem exists_preWienerMeasure : | |
| ∃ ν : Measure (ℝ≥0 → ℝ), IsProbabilityMeasure ν ∧ | |
| IsProjectiveLimit ν BrownianReal.projectiveFamily := | |
| CountableProjective.exists_projective_limit BrownianReal.projectiveFamily | |
| BrownianReal.isProjectiveMeasureFamily_projectiveFamily | |
| def preWienerMeasure : Measure (ℝ≥0 → ℝ) := Classical.choose exists_preWienerMeasure | |
| instance : IsProbabilityMeasure preWienerMeasure := | |
| (Classical.choose_spec exists_preWienerMeasure).1 | |
| theorem preWienerMeasure_projectiveLimit : | |
| IsProjectiveLimit preWienerMeasure BrownianReal.projectiveFamily := | |
| (Classical.choose_spec exists_preWienerMeasure).2 | |
| theorem coordinate_isPreBrownianReal : | |
| IsPreBrownianReal (fun t (ω : ℝ≥0 → ℝ) => ω t) preWienerMeasure where | |
| hasLaw I := { | |
| aemeasurable := (Finset.measurable_restrict I).aemeasurable | |
| map_eq := preWienerMeasure_projectiveLimit I } | |
| end Problem367.BrownianExistence | |
| end | |
| end OAI | |