Theorems · Definition · measure theory
MeasureTheory.OuterMeasure.IsMetric
{X : Type u_2} → [EMetricSpace X] → MeasureTheory.OuterMeasure X → PropWe say that an outer measure μ in an (e)metric space is metric if μ (s ∪ t) = μ s + μ t
for any two metric separated sets s, t.
- Defined in
- Mathlib.MeasureTheory.Measure.Hausdorff
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- EMetricSpacestatement and proof · cited by 242
- Metric.AreSeparatedproof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodorystatement and proof · cited by 1
- MeasureTheory.OuterMeasure.IsMetric.finset_iUnion_of_pairwise_separatedstatement and proof · cited by 1
- MeasureTheory.OuterMeasure.mkMetric'_isMetricstatement · cited by 0
- MeasureTheory.OuterMeasure.IsMetric.le_caratheodorystatement and proof · cited by 0