Theorems · Definition · probability
MeasureTheory.levyProkhorovDist
{Ω : Type u_1} →
[inst : MeasurableSpace Ω] → [PseudoEMetricSpace Ω] → MeasureTheory.Measure Ω → MeasureTheory.Measure Ω → ℝThe Lévy-Prokhorov distance between finite measures:
d(μ,ν) = inf {r ≥ 0 | ∀ B, μ B ≤ ν Bᵣ + r ∧ ν B ≤ μ Bᵣ + r}.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.toRealproof · cited by 859
- MeasureTheory.levyProkhorovEDistproof · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.LevyProkhorov.dist_probabilityMeasure_defstatement · cited by 2
- MeasureTheory.levyProkhorovDist_le_of_forall_lestatement · cited by 1
- MeasureTheory.LevyProkhorov.dist_finiteMeasure_defstatement · cited by 0
- MeasureTheory.levyProkhorovDist_commstatement · cited by 0
- MeasureTheory.levyProkhorovDist_selfstatement · cited by 0
- MeasureTheory.levyProkhorovDist_trianglestatement and proof · cited by 0