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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)
Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Metric
Cited by
15 results in Mathlib
Foundations
Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoMetricSpaceMeasurableSpaceOpensMeasurableSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.measure_le_eq_lt · cited by 3MeasureTheory.measure_le_…InnerProductSpace.volume_ball · cited by 3InnerProductSpace.volume_…MeasureTheory.measure_lt_one_eq_integral_div_gamma · cited by 3MeasureTheory.measure_lt_…AddCircle.closedBall_ae_eq_ball · cited by 2AddCircle.closedBall_ae_e…EuclideanSpace.volume_ball · cited by 2EuclideanSpace.volume_ballBesicovitch.card_le_of_separated · cited by 2Besicovitch.card_le_of_se…MeasureTheory.Measure.addHaar_sphere_of_ne_zero · cited by 1Measure.addHaar_sphere_of…MeasureTheory.integrableOn_fun_norm_addHaar · cited by 1MeasureTheory.integrableO…AddCircle.isAddFundamentalDomain_of_ae_ball · cited by 1AddCircle.isAddFundamenta…MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le · cited by 1SeparableSpace.exists_mea…MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball · cited by 1Measure.toSphereBallBound…AddMonoidHom.exists_nhds_isBounded · cited by 1AddMonoidHom.exists_nhds_…MeasureTheory.ProbabilityMeasure.continuous_pi · cited by 0ProbabilityMeasure.contin…MeasureTheory.ProbabilityMeasure.continuous_prod · cited by 0ProbabilityMeasure.contin…MonoidHom.exists_nhds_isBounded · cited by 0MonoidHom.exists_nhds_isB…Real · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasurableSet · cited by 3075MeasurableSetPseudoMetricSpace · cited by 1550PseudoMetricSpaceMetric.ball · cited by 735Metric.ballOpensMeasurableSpace · cited by 636OpensMeasurableSpaceIsOpen.measurableSet · cited by 82IsOpen.measurableSetMetric.isOpen_ball · cited by 63Metric.isOpen_ballmeasurableSet_ballCITED BYCITES

Cites8

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Cited by15

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