Theorems · Theorem · measure theory
MeasureTheory.measure_ball_lt_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} [inst : PseudoMetricSpace α] [ProperSpace α] {μ : MeasureTheory.Measure α}
[MeasureTheory.IsFiniteMeasureOnCompacts μ] {x : α} {r : ℝ}, μ (Metric.ball x r) < ⊤- Cited by
- 4 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.
Cites13
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
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement · cited by 735
- ProperSpacestatement and proof · cited by 190
- Ne.lt_topproof · cited by 161
- MeasureTheory.IsFiniteMeasureOnCompactsstatement and proof · cited by 109
Cited by4
Results whose statement or proof uses this declaration.
- Besicovitch.card_le_of_separatedproof · cited by 2
- finite_integral_one_add_normproof · cited by 1
- MeasureTheory.Measure.addHaar_sphere_of_ne_zeroproof · cited by 1
- MeasureTheory.measure_unitBall_eq_integral_div_gammaproof · cited by 1