Theorems · Theorem · measure theory
MeasureTheory.ae_eq_top
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
{μ : F}, MeasureTheory.ae μ = ⊤ ↔ ∀ (a : α), μ {a} ≠ 0- Defined in
- Mathlib.MeasureTheory.OuterMeasure.AE
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- Filterstatement · cited by 8,121
- Set.univproof · cited by 3,945
- Compl.complproof · cited by 2,925
- Set.Nonemptyproof · cited by 2,627
- FunLikestatement and proof · cited by 2,560
- MeasureTheory.aestatement · cited by 2,352
- compl_complproof · cited by 229
- Set.singleton_subset_iffproof · cited by 206
Cited by4
Results whose statement or proof uses this declaration.
- essSup_eq_iSupproof · cited by 2
- essSup_eq_ciSupproof · cited by 2
- essInf_eq_ciInfproof · cited by 2
- essInf_eq_iInfproof · cited by 1