Theorems · Theorem · measure theory
MeasureTheory.ae_all_iff
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
{μ : F} {ι : Sort u_4} [Countable ι] {p : α → ι → Prop},
(∀ᵐ (a : α) ∂μ, ∀ (i : ι), p a i) ↔ ∀ (i : ι), ∀ᵐ (a : α) ∂μ, p a i- Defined in
- Mathlib.MeasureTheory.OuterMeasure.AE
- Cited by
- 70 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Countablestatement and proof · cited by 633
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
- eventually_countable_forallproof · cited by 7
Cited by70
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_lt_topproof · cited by 21
- aestronglyMeasurable_of_tendsto_aeproof · cited by 9
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- MeasureTheory.MemLp.isProbabilityMeasure_of_indepFunproof · cited by 5
- ProbabilityTheory.preCDF_le_oneproof · cited by 4
- ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_forall_integrable_exp_mulproof · cited by 4
- ProbabilityTheory.Kernel.IndepFun.process_congr_leftproof · cited by 4
- MeasureTheory.tendstoInMeasure_of_tendsto_aeproof · cited by 4
- aeSeq.aeSeq_n_eq_fun_n_aeproof · cited by 3
- MeasureTheory.ae_eq_of_ae_le_of_lintegral_leproof · cited by 3
- ProbabilityTheory.IsRatCondKernelCDFAux.nonnegproof · cited by 3
- MeasureTheory.ae_norm_ofReal_f_le_boundproof · cited by 3