Theorems · Theorem · approximation theory
Asymptotics.isBigOWith_norm_left
∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {c : ℝ} {g : α → F}
{f' : α → E'} {l : Filter α}, Asymptotics.IsBigOWith c l (fun x => ‖f' x‖) g ↔ Asymptotics.IsBigOWith c l f' g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormSeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallyproof · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOWithstatement · cited by 187
- norm_normproof · cited by 113
- Asymptotics.IsBigOWith_defproof · cited by 46
Cited by6
Results whose statement or proof uses this declaration.
- Asymptotics.isBigO_norm_leftproof · cited by 11
- Asymptotics.isLittleO_norm_leftproof · cited by 7
- Asymptotics.isBigOWith_abs_leftproof · cited by 3
- Asymptotics.isBigOWith_norm_normproof · cited by 2
- Asymptotics.IsBigOWith.norm_leftproof · cited by 0
- Asymptotics.IsBigOWith.of_norm_leftproof · cited by 0