Theorems · Theorem · measure theory
MeasureTheory.ae_iff
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
{μ : F} {p : α → Prop}, (∀ᵐ (a : α) ∂μ, p a) ↔ μ {a | ¬p a} = 0- Defined in
- Mathlib.MeasureTheory.OuterMeasure.AE
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 135 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredstatement · cited by 6,101
- Filter.Eventuallystatement · cited by 3,134
- FunLikestatement and proof · cited by 2,560
- MeasureTheory.aestatement · cited by 2,352
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
Cited by26
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_of_ae_restrict_of_ae_restrict_complproof · cited by 14
- MeasureTheory.Measure.ae_smul_measureproof · cited by 10
- MeasureTheory.SimpleFunc.setToSimpleFunc_congrproof · cited by 10
- MeasureTheory.StronglyMeasurable.ae_eq_trim_of_stronglyMeasurableproof · cited by 7
- Polynomial.mahlerMeasure_mulproof · cited by 5
- MeasureTheory.TendstoInMeasure.exists_seq_tendsto_aeproof · cited by 5
- MeasureTheory.withDensity_absolutelyContinuous'proof · cited by 5
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_eq_of_sigmaFiniteproof · cited by 3
- MeasureTheory.ae_withDensity_iff'proof · cited by 3
- MeasureTheory.withDensity_apply_eq_zero'proof · cited by 2
- ae_eq_trim_of_measurableproof · cited by 2
- ProbabilityTheory.Kernel.ae_comp_of_ae_aeproof · cited by 2