Theorems · Definition · measure theory

VitaliFamily.limRatio

{α : Type u_1} →
  [inst : PseudoMetricSpace α] →
    {m0 : MeasurableSpace α} → {μ : MeasureTheory.Measure α} → VitaliFamily μ → MeasureTheory.Measure α → α → ENNReal

The limit along a Vitali family of ρ a / μ a where it makes sense, and garbage otherwise. Do not use this definition: it is only a temporary device to show that this ratio tends almost everywhere to the Radon-Nikodym derivative.

Defined in

Mathlib.MeasureTheory.Covering.Differentiation

Cited by

4 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace