Theorems · Theorem · measure theory

MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
  [FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] (s : Set E) (x : E),
  Filter.Tendsto (fun r => μ (s ∩ Metric.closedBall x r) / μ (Metric.closedBall x r)) (nhdsWithin 0 (Set.Ioi 0))
      (nhds 0) →
    ∀ (t u : Set E),
      μ u ≠ 0 →
        t ⊆ Metric.closedBall 0 1 →
          Filter.Tendsto (fun r => μ (s ∩ ({x} + r • t)) / μ ({x} + r • u)) (nhdsWithin 0 (Set.Ioi 0)) (nhds 0)

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

1 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasure