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Theorems · Theorem · approximation theory

Asymptotics.IsLittleO.comp_tendsto

∀ {α : Type u_1} {β : Type u_2} {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 → ∀ {k : β → α} {l' : Filter β}, Filter.Tendsto k l' l → (f ∘ k) =o[l'] (g ∘ k)
Defined in
Mathlib.Analysis.Asymptotics.Defs
Cited by
18 results in Mathlib
Foundations
Depth 106 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.

Filter.Tendsto.integral_sub_linear_isLittleO_ae · cited by 3Tendsto.integral_sub_line…isLittleO_log_rpow_atTop · cited by 3isLittleO_log_rpow_atTopHasFDerivAt.comp_semilinear · cited by 3HasFDerivAt.comp_semiline…cexp_neg_quadratic_isLittleO_abs_rpow_cocompact · cited by 2cexp_neg_quadratic_isLitt…Asymptotics.IsLittleO.natCast_atTop · cited by 2IsLittleO.natCast_atTopProbabilityTheory.tendsto_charFun_inv_sqrt_mul_pow · cited by 1ProbabilityTheory.tendsto…Asymptotics.isLittleO_pow_sub_pow_sub · cited by 1Asymptotics.isLittleO_pow…Complex.IsExpCmpFilter.isLittleO_im_pow_exp_re · cited by 1IsExpCmpFilter.isLittleO_…Complex.IsExpCmpFilter.isLittleO_log_re_re · cited by 1IsExpCmpFilter.isLittleO_…Complex.IsExpCmpFilter.of_isBigO_im_re_rpow · cited by 1IsExpCmpFilter.of_isBigO_…Asymptotics.IsEquivalent.comp_tendsto · cited by 1IsEquivalent.comp_tendstoisLittleO_abs_log_rpow_rpow_nhdsGT_zero · cited by 1isLittleO_abs_log_rpow_rp…ProbabilityTheory.strong_law_aux4 · cited by 1ProbabilityTheory.strong_…ProbabilityTheory.strong_law_aux6 · cited by 1ProbabilityTheory.strong_…isBigO_rpow_zero_log_smul · cited by 1isBigO_rpow_zero_log_smulReal · cited by 25697RealFilter · cited by 8121FilterFilter.Tendsto · cited by 3814Filter.TendstoNorm · cited by 512NormAsymptotics.IsLittleO · cited by 375Asymptotics.IsLittleOAsymptotics.IsLittleO.of_isBigOWith · cited by 12IsLittleO.of_isBigOWithAsymptotics.IsLittleO.forall_isBigOWith · cited by 10IsLittleO.forall_isBigOWi…Asymptotics.IsBigOWith.comp_tendsto · cited by 4IsBigOWith.comp_tendstoIsLittleO.comp_tendstoCITED BYCITES

Cites8

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Cited by18

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