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Theorems · Theorem · approximation theory

Asymptotics.IsLittleO.isBigO

∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {f : α → E} {g : α → F} {l : Filter α},
  f =o[l] g → f =O[l] g
Defined in
Mathlib.Analysis.Asymptotics.Defs
Cited by
35 results in Mathlib
Foundations
Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormNorm

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Asymptotics.IsEquivalent.isBigO · cited by 13IsEquivalent.isBigOReal.GammaIntegral_convergent · cited by 5Real.GammaIntegral_conver…TFAE_exists_lt_isLittleO_pow · cited by 4TFAE_exists_lt_isLittleO_…Complex.tsum_exp_neg_quadratic · cited by 3Complex.tsum_exp_neg_quad…summable_norm_mul_geometric_of_norm_lt_one · cited by 2summable_norm_mul_geometr…Real.isBigO_log_const_mul_log_atTop · cited by 2Real.isBigO_log_const_mul…Filter.ZeroAtFilter.boundedAtFilter · cited by 2ZeroAtFilter.boundedAtFil…FormalMultilinearSeries.min_radius_le_radius_add · cited by 2FormalMultilinearSeries.m…UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left · cited by 2IsZeroAtImInfty.petersson…AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_ge · cited by 1AkraBazziRecurrence.rpow_…AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_le · cited by 1AkraBazziRecurrence.rpow_…Asymptotics.isLittleO_zero_right_iff · cited by 1Asymptotics.isLittleO_zer…ContinuousAt.isBigO · cited by 1ContinuousAt.isBigOFunction.locallyFinsuppWithin.logCounting_single_isBigO_log · cited by 1locallyFinsuppWithin.logC…Complex.hasDerivAt_GammaIntegral · cited by 1Complex.hasDerivAt_GammaI…Filter · cited by 8121FilterNorm · cited by 512NormAsymptotics.IsBigO · cited by 506Asymptotics.IsBigOAsymptotics.IsLittleO · cited by 375Asymptotics.IsLittleOAsymptotics.IsBigOWith.isBigO · cited by 40IsBigOWith.isBigOAsymptotics.IsLittleO.isBigOWith · cited by 2IsLittleO.isBigOWithIsLittleO.isBigOCITED BYCITES

Cites6

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Cited by35

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