Theorems · Definition · measure theory

VitaliFamily.limRatioMeas

{α : Type u_1} →
  [inst : PseudoMetricSpace α] →
    {m0 : MeasurableSpace α} →
      {μ : MeasureTheory.Measure α} →
        VitaliFamily μ →
          [SecondCountableTopology α] →
            [BorelSpace α] →
              [MeasureTheory.IsLocallyFiniteMeasure μ] →
                {ρ : MeasureTheory.Measure α} →
                  [MeasureTheory.IsLocallyFiniteMeasure ρ] → ρ.AbsolutelyContinuous μ → α → ENNReal

A measurable version of v.limRatio ρ. Do not use this definition: it is only a temporary device to show that v.limRatio is almost everywhere equal to the Radon-Nikodym derivative.

Defined in

Mathlib.MeasureTheory.Covering.Differentiation

Cited by

11 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceSecondCountableTopologyBorelSpaceMeasureTheory.IsLocallyFiniteMeasureMeasureTheory.IsLocallyFiniteMeasure