Theorems · Theorem · measure theory
Metric.measure_closedEBall_pos
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : MeasureTheory.Measure X)
[μ.IsOpenPosMeasure] (x : X) {r : ENNReal}, r ≠ 0 → 0 < μ (Metric.closedEBall x r)- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LT.lt.trans_leproof · cited by 678
- MeasureTheory.measure_monoproof · cited by 338
- Metric.closedEBallstatement · cited by 107
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
- Metric.eball_subset_closedEBallproof · cited by 5
- Metric.measure_eball_posproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- EMetric.measure_closedBall_posproof · cited by 0