Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.tendsto_div_nhds_zero
∀ {α : Type u_1} {𝕜 : Type u_15} [inst : NormedDivisionRing 𝕜] {l : Filter α} {f g : α → 𝕜},
f =o[l] g → Filter.Tendsto (fun x => f x / g x) l (nhds 0)- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Norm.normproof · cited by 5,413
- Filter.Tendstostatement · cited by 3,814
- div_eq_mul_invproof · cited by 715
- Asymptotics.IsLittleOstatement and proof · cited by 375
- NormedDivisionRingstatement and proof · cited by 360
- NormOneClass.norm_oneproof · cited by 148
- norm_divproof · cited by 53
- Asymptotics.isBigO_reflproof · cited by 51
- Asymptotics.isLittleO_one_iffproof · cited by 20
- Asymptotics.isBigO_of_leproof · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_iff_tendsto'proof · cited by 7
- Asymptotics.isEquivalent_iff_tendsto_oneproof · cited by 3
- Asymptotics.isLittleO_iff_exists_eq_mulproof · cited by 3
- NormedRing.inverse_continuousAtproof · cited by 3
- Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zeroproof · cited by 2
- tendsto_pow_const_div_const_pow_of_one_ltproof · cited by 2
- tendsto_log_div_rpow_nhdsGT_zeroproof · cited by 1