Theorems · Theorem · measure theory
Set.Countable.measure_zero
∀ {α : Type u_1} {m0 : MeasurableSpace α} {s : Set α},
s.Countable → ∀ (μ : MeasureTheory.Measure α) [MeasureTheory.NullSingletonClass μ], μ s = 0- Cited by
- 9 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Countablestatement and proof · cited by 545
- MeasureTheory.NullSingletonClassstatement and proof · cited by 125
- MeasureTheory.NullSingletonClass.measure_singletonproof · cited by 47
- Set.biUnion_of_singletonproof · cited by 43
- MeasureTheory.measure_biUnion_null_iffproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- Set.Finite.measure_zeroproof · cited by 9
- Set.Countable.ae_notMemproof · cited by 6
- ae_restrict_le_codiscreteWithinproof · cited by 4
- MeasureTheory.meas_le_ae_eq_meas_ltproof · cited by 4
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- MeasureTheory.exists_null_frontier_thickeningproof · cited by 3
- MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOnproof · cited by 2
- MeasureTheory.exists_accPt_of_nullSingletonClassproof · cited by 1