Theorems · Theorem · measure theory
Metric.measure_eball_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.eball x r)- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 173 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
- Metric.eballstatement · cited by 294
- Ne.bot_ltproof · cited by 116
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
- IsOpen.measure_posproof · cited by 18
- Metric.isOpen_eballproof · cited by 13
- Metric.mem_eball_selfproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Metric.measure_closedEBall_posproof · cited by 1
- EMetric.measure_ball_posproof · cited by 0