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
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.
- Realproof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement and proof · cited by 3,814
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsLittleO.of_isBigOWithproof · cited by 12
- Asymptotics.IsLittleO.forall_isBigOWithproof · cited by 10
- Asymptotics.IsBigOWith.comp_tendstoproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- Filter.Tendsto.integral_sub_linear_isLittleO_aeproof · cited by 3
- isLittleO_log_rpow_atTopproof · cited by 3
- HasFDerivAt.comp_semilinearproof · cited by 3
- cexp_neg_quadratic_isLittleO_abs_rpow_cocompactproof · cited by 2
- Asymptotics.IsLittleO.natCast_atTopproof · cited by 2
- ProbabilityTheory.tendsto_charFun_inv_sqrt_mul_powproof · cited by 1
- Asymptotics.isLittleO_pow_sub_pow_subproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_im_pow_exp_reproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_re_reproof · cited by 1
- Complex.IsExpCmpFilter.of_isBigO_im_re_rpowproof · cited by 1
- Asymptotics.IsEquivalent.comp_tendstoproof · cited by 1
- isLittleO_abs_log_rpow_rpow_nhdsGT_zeroproof · cited by 1