Theorems · Theorem · measure theory

MeasureTheory.OuterMeasure.IsMetric.finset_iUnion_of_pairwise_separated

∀ {ι : Type u_1} {X : Type u_2} [inst : EMetricSpace X] {μ : MeasureTheory.OuterMeasure X},
  μ.IsMetric →
    ∀ {I : Finset ι} {s : ι → Set X},
      (∀ i ∈ I, ∀ j ∈ I, i ≠ j → Metric.AreSeparated (s i) (s j)) → μ (⋃ i ∈ I, s i) = ∑ i ∈ I, μ (s i)

A metric outer measure is additive on a finite set of pairwise metric separated sets.

Defined in

Mathlib.MeasureTheory.Measure.Hausdorff

Cited by

1 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EMetricSpace