Theorems · Theorem · probability

MeasureTheory.measure_le_measure_closure_of_levyProkhorovEDist_eq_zero

∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : PseudoEMetricSpace Ω] [OpensMeasurableSpace Ω]
  {μ ν : MeasureTheory.Measure Ω},
  MeasureTheory.levyProkhorovEDist μ ν = 0 →
    ∀ {s : Set Ω}, MeasurableSet s → (∃ δ > 0, ν (Metric.thickening δ s) ≠ ⊤) → μ s ≤ ν (closure s)

Defined in

Mathlib.MeasureTheory.Measure.LevyProkhorovMetric

Cited by

1 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpacePseudoEMetricSpaceOpensMeasurableSpace