Mathlib Map

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] g

Alias 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.

IsBoundedBilinearMap.continuous · cited by 11IsBoundedBilinearMap.cont…mellinConvergent_of_isBigO_rpow · cited by 3mellinConvergent_of_isBig…intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae · cited by 2intervalIntegral.integral…ContinuousLinearMap.bilinear_hasTemperateGrowth · cited by 2ContinuousLinearMap.bilin…FormalMultilinearSeries.taylorComp_sub_taylorComp_isBigO · cited by 2FormalMultilinearSeries.t…intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae · cited by 2intervalIntegral.integral…UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left · cited by 2IsZeroAtImInfty.petersson…mellin_hasDerivAt_of_isBigO_rpow · cited by 2mellin_hasDerivAt_of_isBi…ModularFormClass.exists_petersson_le · cited by 1ModularFormClass.exists_p…UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right · cited by 1IsZeroAtImInfty.petersson…ContDiffPointwiseHolderAt.prodMk · cited by 1ContDiffPointwiseHolderAt…Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO · cited by 1Complex.dist_le_mul_div_p…PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decay · cited by 1PhragmenLindelof.eq_zero_…ContDiffPointwiseHolderAt.fderiv · cited by 1ContDiffPointwiseHolderAt…ModularGroup.exists_bound_of_subgroup_invariant_of_isBigO · cited by 1ModularGroup.exists_bound…Real · cited by 25697RealFilter · cited by 8121FilterNorm.norm · cited by 5413Norm.normSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNorm · cited by 512NormAsymptotics.IsBigO · cited by 506Asymptotics.IsBigOAsymptotics.isBigO_norm_left · cited by 11Asymptotics.isBigO_norm_l…IsBigO.norm_leftCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.