Theorems · Theorem · approximation theory

Asymptotics.IsBigOWith.of_bound

∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {c : ℝ} {f : α → E} {g : α → F}
  {l : Filter α}, (∀ᶠ (x : α) in l, ‖f x‖ ≤ c * ‖g x‖) → Asymptotics.IsBigOWith c l f g

Alias of the reverse direction of Asymptotics.isBigOWith_iff. Definition of IsBigOWith. We record it in a lemma as IsBigOWith is irreducible.

Defined in

Mathlib.Analysis.Asymptotics.Defs

Cited by

16 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormNorm