Theorems · Theorem · measure theory
measurableSet_ball
∀ {α : Type u_1} [inst : PseudoMetricSpace α] [inst_1 : MeasurableSpace α] [OpensMeasurableSpace α] {x : α} {ε : ℝ},
MeasurableSet (Metric.ball x ε)- Cited by
- 15 results in Mathlib
- Foundations
- Depth 119 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.ballstatement · cited by 735
- OpensMeasurableSpacestatement and proof · cited by 636
- IsOpen.measurableSetproof · cited by 82
- Metric.isOpen_ballproof · cited by 63
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_le_eq_ltproof · cited by 3
- InnerProductSpace.volume_ballproof · cited by 3
- MeasureTheory.measure_lt_one_eq_integral_div_gammaproof · cited by 3
- AddCircle.closedBall_ae_eq_ballproof · cited by 2
- EuclideanSpace.volume_ballproof · cited by 2
- Besicovitch.card_le_of_separatedproof · cited by 2
- MeasureTheory.Measure.addHaar_sphere_of_ne_zeroproof · cited by 1
- MeasureTheory.integrableOn_fun_norm_addHaarproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- MeasureTheory.SeparableSpace.exists_measurable_partition_diam_leproof · cited by 1
- AddMonoidHom.exists_nhds_isBoundedproof · cited by 1