Theorems · Theorem · measure theory

VitaliFamily.measure_limRatioMeas_zero

∀ {α : Type u_1} [inst : PseudoMetricSpace α] {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  (v : VitaliFamily μ) [inst_1 : SecondCountableTopology α] [inst_2 : BorelSpace α]
  [inst_3 : MeasureTheory.IsLocallyFiniteMeasure μ] {ρ : MeasureTheory.Measure α}
  [inst_4 : MeasureTheory.IsLocallyFiniteMeasure ρ] (hρ : ρ.AbsolutelyContinuous μ), ρ (v.limRatioMeas hρ ⁻¹' {0}) = 0

The points with v.limRatioMeas hρ x = 0 have measure 0 for ρ.

Defined in

Mathlib.MeasureTheory.Covering.Differentiation

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceSecondCountableTopologyBorelSpaceMeasureTheory.IsLocallyFiniteMeasureMeasureTheory.IsLocallyFiniteMeasure