Theorems · Theorem · approximation theory

Asymptotics.IsLittleO.bound

∀ {α : Type u_1} {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 → ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : α) in l, ‖f x‖ ≤ c * ‖g x‖

Alias of the forward direction of Asymptotics.isLittleO_iff. Definition of IsLittleO in terms of filters.

Defined in

Mathlib.Analysis.Asymptotics.Defs

Cited by

4 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormNorm