Theorems · Theorem · approximation theory
Asymptotics.isLittleO_one_left_iff
∀ {α : Type u_1} {E : Type u_3} (F : Type u_4) [inst : Norm E] [inst_1 : Norm F] {f : α → E} {l : Filter α}
[inst_2 : One F] [NormOneClass F], (fun _x => 1) =o[l] f ↔ Filter.Tendsto (fun x => ‖f x‖) l Filter.atTop- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormNormOneNormOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- Filter.atTopstatement · cited by 2,405
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement · cited by 375
- NormOneClass.norm_oneproof · cited by 148
- NormOneClassstatement and proof · cited by 136
- Filter.HasBasis.tendsto_right_iffproof · cited by 81
Cited by3
Results whose statement or proof uses this declaration.
- AkraBazziRecurrence.isLittleO_deriv_smoothingFnproof · cited by 2
- Asymptotics.isLittleO_const_left_of_neproof · cited by 2
- Asymptotics.IsEquivalent.logproof · cited by 0