Theorems · Theorem · measure theory
measurableSet_closedBall
∀ {α : Type u_1} [inst : PseudoMetricSpace α] [inst_1 : MeasurableSpace α] [OpensMeasurableSpace α] {x : α} {ε : ℝ},
MeasurableSet (Metric.closedBall x ε)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasurableSetstatement · cited by 3,075
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- OpensMeasurableSpacestatement and proof · cited by 636
- IsClosed.measurableSetproof · cited by 65
- Metric.isClosed_closedBallproof · cited by 28
Cited by13
Results whose statement or proof uses this declaration.
- AddCircle.volume_closedBallproof · cited by 4
- ApproximatesLinearOn.norm_fderiv_sub_leproof · cited by 3
- MeasureTheory.measure_le_eq_ltproof · cited by 3
- ContDiffBump.measure_closedBall_le_integralproof · cited by 2
- NormedAddCommGroup.exists_norm_nsmul_leproof · cited by 1
- ExistsContDiffBumpBase.y_pos_of_mem_ballproof · cited by 1
- MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translatesproof · cited by 1
- MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zeroproof · cited by 1
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1
- MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero_auxproof · cited by 1
- Besicovitch.exist_finset_disjoint_balls_large_measureproof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_leproof · cited by 1