Theorems · Theorem · approximation theory
Asymptotics.isLittleO_of_tendsto
∀ {α : Type u_1} {𝕜 : Type u_15} [inst : NormedDivisionRing 𝕜] {l : Filter α} {f g : α → 𝕜},
(∀ (x : α), g x = 0 → f x = 0) → Filter.Tendsto (fun x => f x / g x) l (nhds 0) → f =o[l] gAlias of the reverse direction of Asymptotics.isLittleO_iff_tendsto.
- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 121 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.
Cites6
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
- Filter.Tendstostatement · cited by 3,814
- Asymptotics.IsLittleOstatement · cited by 375
- NormedDivisionRingstatement and proof · cited by 360
- Asymptotics.isLittleO_iff_tendstoproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- isLittleO_pow_pow_of_lt_leftproof · cited by 5
- AkraBazziRecurrence.isLittleO_smoothingFn_oneproof · cited by 3
- Real.Gamma_integrand_isLittleOproof · cited by 2
- isLittleO_rpow_exp_pos_mul_atTopproof · cited by 2
- isLittleO_exp_mul_rpow_of_ltproof · cited by 1