Theorems · Theorem · measure theory
EMetric.measure_closedBall_pos
Deprecated since 2026-01-24Use Metric.measure_closedEBall_pos instead.
∀ {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)Alias of Metric.measure_closedEBall_pos.
- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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 · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement · cited by 1,536
- Metric.closedEBallstatement · cited by 107
- MeasureTheory.Measure.IsOpenPosMeasurestatement · cited by 80
- Metric.measure_closedEBall_posproof · cited by 1
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