Theorems · Theorem · measure theory
MeasureTheory.measure_closedBall_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.closedBall x r) < ⊤- Cited by
- 6 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.
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.closedBallstatement · cited by 704
- ProperSpacestatement and proof · cited by 190
- MeasureTheory.IsFiniteMeasureOnCompactsstatement and proof · cited by 109
- Metric.isBounded_closedBallproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_auxproof · cited by 1
- ContDiffBump.normed_le_div_measure_closedBall_rOutproof · cited by 1
- ContDiffBump.normed_le_div_measure_closedBall_rInproof · cited by 0
- MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zeroproof · cited by 0