Theorems · Theorem · measure theory

VitaliFamily.ae_tendsto_limRatioMeas

∀ {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),
  ∀ᵐ (x : α) ∂μ, Filter.Tendsto (fun a => ρ a / μ a) (v.filterAt x) (nhds (v.limRatioMeas hρ x))

Defined in

Mathlib.MeasureTheory.Covering.Differentiation

Cited by

3 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceSecondCountableTopologyBorelSpaceMeasureTheory.IsLocallyFiniteMeasureMeasureTheory.IsLocallyFiniteMeasure