Theorems · Theorem · approximation theory
Asymptotics.isLittleO_iff_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) → (f =o[l] g ↔ Filter.Tendsto (fun x => f x / g x) l (nhds 0))- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 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.
Cites7
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
- Filter.Eventually.of_forallproof · cited by 526
- Asymptotics.IsLittleOstatement · cited by 375
- NormedDivisionRingstatement and proof · cited by 360
- Asymptotics.isLittleO_iff_tendsto'proof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_of_tendstoproof · cited by 5
- Complex.hasSum_taylorSeries_logproof · cited by 2
- hasFDerivAtFilter_iff_tendstoproof · cited by 1
- taylor_tendstoproof · cited by 1
- Real.isLittleO_pow_exp_atTopproof · cited by 0