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}, f' =O[l] g → (fun x => ‖f' x‖) =O[l] gAlias of the reverse direction of Asymptotics.isBigO_norm_left.
- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 116 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.
Cites7
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 · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.isBigO_norm_leftproof · cited by 11
Cited by15
Results whose statement or proof uses this declaration.
- IsBoundedBilinearMap.continuousproof · cited by 11
- mellinConvergent_of_isBigO_rpowproof · cited by 3
- intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_aeproof · cited by 2
- ContinuousLinearMap.bilinear_hasTemperateGrowthproof · cited by 2
- FormalMultilinearSeries.taylorComp_sub_taylorComp_isBigOproof · cited by 2
- intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_aeproof · cited by 2
- UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_leftproof · cited by 2
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- ModularFormClass.exists_petersson_leproof · cited by 1
- UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_rightproof · cited by 1
- ContDiffPointwiseHolderAt.prodMkproof · cited by 1
- Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleOproof · cited by 1