Theorems · Definition · measure theory

Besicovitch.vitaliFamily

{α : Type u_1} →
  [inst : MetricSpace α] →
    [SecondCountableTopology α] →
      [inst_2 : MeasurableSpace α] →
        [OpensMeasurableSpace α] →
          [HasBesicovitchCovering α] → (μ : MeasureTheory.Measure α) → [MeasureTheory.SFinite μ] → VitaliFamily μ

In a space with the Besicovitch covering property, the set of closed balls with positive radius forms a Vitali family. This is essentially a restatement of the measurable Besicovitch theorem.

Defined in

Mathlib.MeasureTheory.Covering.Besicovitch

Cited by

5 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MetricSpaceSecondCountableTopologyMeasurableSpaceOpensMeasurableSpaceHasBesicovitchCoveringMeasureTheory.SFinite