Theorems · Theorem · measure theory
MeasurableSingletonClass.measurableSet_singleton
∀ {α : Type u_7} {inst : MeasurableSpace α} [self : MeasurableSingletonClass α] (x : α), MeasurableSet {x}A singleton is a measurable set.
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- MeasurableSingletonClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasurableSetstatement · cited by 3,075
- MeasurableSingletonClassstatement and proof · cited by 230
Cited by53
Results whose statement or proof uses this declaration.
- measurableSet_setOfPredproof · cited by 19
- MeasurableSet.singletonproof · cited by 19
- MeasureTheory.Measure.dirac_applyproof · cited by 9
- ProbabilityTheory.Kernel.measurable_rnDerivAuxproof · cited by 8
- measurable_of_tendsto_metrizable'proof · cited by 7
- MeasureTheory.setIntegral_pos_iff_support_of_nonneg_aeproof · cited by 6
- measurableSet_supportproof · cited by 5
- ProbabilityTheory.Kernel.measure_mutuallySingularSetSliceproof · cited by 4
- ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSliceproof · cited by 4
- MeasureTheory.nullMeasurableSet_singletonproof · cited by 4
- ProbabilityTheory.avgRisk_countable'proof · cited by 3
- MeasureTheory.ae_eq_dirac'proof · cited by 3