Theorems · Theorem · measure theory

VitaliFamily.limRatioMeas.congr_simp

∀ {α : Type u_1} [inst : PseudoMetricSpace α] {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  (v v_1 : VitaliFamily μ),
  v = v_1 →
    ∀ [inst_1 : SecondCountableTopology α] [inst_2 : BorelSpace α] [inst_3 : MeasureTheory.IsLocallyFiniteMeasure μ]
      {ρ ρ_1 : MeasureTheory.Measure α} (e_ρ : ρ = ρ_1) [inst_4 : MeasureTheory.IsLocallyFiniteMeasure ρ]
      (hρ : ρ.AbsolutelyContinuous μ) (a a_1 : α), a = a_1 → v.limRatioMeas hρ a = v_1.limRatioMeas ⋯ a_1

Defined in

Mathlib.MeasureTheory.Covering.Differentiation

Cited by

0 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpaceSecondCountableTopologyBorelSpaceMeasureTheory.IsLocallyFiniteMeasureMeasureTheory.IsLocallyFiniteMeasure