Theorems · Theorem · measure theory
MeasureTheory.measure_eq_zero_iff_ae_notMem
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
{μ : F} {s : Set α}, μ s = 0 ↔ ∀ᵐ (a : α) ∂μ, a ∉ s- Defined in
- Mathlib.MeasureTheory.OuterMeasure.AE
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 138 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
- 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
- MeasureTheory.compl_mem_ae_iffproof · cited by 9
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_mono_aeproof · cited by 36
- MeasureTheory.Measure.ae_le_iff_absolutelyContinuousproof · cited by 7
- MeasureTheory.lintegral_eq_nnrealproof · cited by 6
- ProbabilityTheory.Kernel.exists_ae_eq_isMarkovKernelproof · cited by 6
- MeasureTheory.Conservative.ae_mem_imp_frequently_image_memproof · cited by 4
- MeasureTheory.pdf.IsUniform.pdf_eqproof · cited by 3
- MeasureTheory.lintegral_iSup_aeproof · cited by 1
- MeasureTheory.Measure.AbsolutelyContinuous.compProd_of_compProdproof · cited by 1
- MeasureTheory.integral_union_eq_left_of_ae_auxproof · cited by 1
- MeasureTheory.Integrable.integral_eq_integral_Ioc_meas_leproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1