| import Mathlib |
| import OAI.Probability.GaussianInformation.Inverse.InverseMoments |
|
|
| namespace OAI |
| open MeasureTheory Metric |
| open scoped ENNReal |
| namespace AllScaleInverseVolume |
| open Set |
| open scoped Topology NNReal |
| open InnerProductSpace |
| open scoped RealInnerProductSpace |
| open InnerProductSpace Matrix MeasureTheory Set |
| open scoped RealInnerProductSpace |
| variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] |
| theorem inverse_volume_without_support : InverseVolumeStatement := by |
| refine ⟨20,by norm_num,300,?_⟩ |
| intro d hd ν hprob hν u |
| have : IsProbabilityMeasure ν := hprob |
| have hd1 : 1 ≤ d := by omega |
| have hk3 : 3 ≤ d/100 := by omega |
| have hk : d/100 ≤ d := Nat.div_le_self _ _ |
| have hk100 : 100*(d/100) ≤ d := by omega |
| have hα : 10*(d/100:ℕ) ≤ ((d:ℝ)-1)/2 := by |
| have hh : 100*(d/100:ℕ) ≤ (d:ℝ) := by exact_mod_cast hk100 |
| have hd' : (300:ℝ) ≤ d := by exact_mod_cast hd |
| nlinarith |
| change (∫⁻ z,rawInverse u z ∂Measure.pi (fun _ : Fin (d/100) => ν)) ≤ _ |
| exact (lintegral_raw_le hd1 hk3 hα ν hν u).trans (inverse_constants hd1 hk) |
|
|
| end AllScaleInverseVolume |
|
|
| end OAI |
|
|
