Theorems · Theorem · approximation theory
Asymptotics.isBigO_norm_left
∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {g : α → F}
{f' : α → E'} {l : Filter α}, (fun x => ‖f' x‖) =O[l] g ↔ f' =O[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 115 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.
Cites8
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsBigO_defproof · cited by 26
- Asymptotics.isBigOWith_norm_leftproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigO.norm_leftproof · cited by 15
- Asymptotics.IsBigO.of_norm_leftproof · cited by 8
- hasFDerivAt_norm_rpowproof · cited by 5
- Asymptotics.isBigO_norm_normproof · cited by 4
- Asymptotics.isBigO_abs_leftproof · cited by 3
- Asymptotics.isBigO_const_smul_leftproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- summable_norm_mul_geometric_of_norm_lt_one'proof · cited by 1
- ContDiffPointwiseHolderAt.zero_order_iffproof · cited by 1
- UpperHalfPlane.IsBoundedAtImInfty.slashproof · cited by 1
- Complex.hasDerivAt_GammaIntegralproof · cited by 1