Theorems · Theorem · approximation theory

Filter.IsBoundedUnder.isLittleO_sub_self_inv

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedField 𝕜] [inst_1 : Norm E] {a : 𝕜} {f : 𝕜 → E},
  Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) (nhdsWithin a {a}ᶜ) (norm ∘ f) →
    f =o[nhdsWithin a {a}ᶜ] fun x => (x - a)⁻¹

If f : 𝕜 → E is bounded in a punctured neighborhood of a, then f(x) = o((x - a)⁻¹) as x → a, x ≠ a.

Defined in

Mathlib.Analysis.Asymptotics.SpecificAsymptotics

Cited by

2 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNorm