Theorems · Theorem · approximation theory
Asymptotics.isLittleO_const_left_of_ne
∀ {α : Type u_1} {F : Type u_4} {E'' : Type u_9} [inst : Norm F] [inst_1 : NormedAddCommGroup E''] {g : α → F}
{l : Filter α} {c : E''}, c ≠ 0 → ((fun _x => c) =o[l] g ↔ Filter.Tendsto (fun x => ‖g x‖) l Filter.atTop)- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormNormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Filterstatement and proof · cited by 8,121
- Norm.normstatement · cited by 5,413
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsBigO.trans_isLittleOproof · cited by 32
- Asymptotics.isBigO_const_constproof · cited by 7
- Asymptotics.isBigO_const_oneproof · cited by 4
- Asymptotics.isLittleO_one_left_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_const_leftproof · cited by 11
- Asymptotics.IsTheta.tendsto_norm_atTop_iffproof · cited by 0