Theorems · Theorem · measure theory
MeasureTheory.NullSingletonClass.measure_singleton
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [self : MeasureTheory.NullSingletonClass μ]
(x : α), μ {x} = 0- Cited by
- 47 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasureTheory.NullSingletonClassstatement and proof · cited by 125
Cited by47
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- MeasureTheory.Ioo_ae_eq_Iocproof · cited by 11
- MeasureTheory.Ioc_ae_eq_Iccproof · cited by 9
- Set.Countable.measure_zeroproof · cited by 9
- MeasureTheory.integral_Icc_eq_integral_Iocproof · cited by 8
- MeasureTheory.Ioo_ae_eq_Iccproof · cited by 7
- integrableOn_Icc_iff_integrableOn_Iocproof · cited by 7
- integrableOn_Ici_iff_integrableOn_Ioiproof · cited by 7
- MeasureTheory.integral_Ioc_eq_integral_Iooproof · cited by 6
- MeasureTheory.Ioi_ae_eq_Iciproof · cited by 5
- MeasureTheory.Ioo_ae_eq_Icoproof · cited by 5
- MeasureTheory.Iio_ae_eq_Iicproof · cited by 4