Theorems · Theorem · measure theory
MeasureTheory.OuterMeasure.IsMetric.le_caratheodory
∀ {X : Type u_2} [inst : EMetricSpace X] {μ : MeasureTheory.OuterMeasure X} [inst_1 : MeasurableSpace X] [BorelSpace X],
μ.IsMetric → inst_1 ≤ μ.caratheodory- Defined in
- Mathlib.MeasureTheory.Measure.Hausdorff
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- EMetricSpacestatement and proof · cited by 242
- MeasureTheory.OuterMeasure.caratheodorystatement and proof · cited by 37
- BorelSpace.measurable_eqproof · cited by 26
- MeasureTheory.OuterMeasure.IsMetricstatement and proof · cited by 4
- MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodoryproof · cited by 1
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