Theorems · Theorem · approximation theory

Asymptotics.IsBigOWith.triangle

∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {c c' : ℝ}
  {g : α → F} {l : Filter α} {f₁ f₂ f₃ : α → E'},
  Asymptotics.IsBigOWith c l (fun x => f₁ x - f₂ x) g →
    Asymptotics.IsBigOWith c' l (fun x => f₂ x - f₃ x) g → Asymptotics.IsBigOWith (c + c') l (fun x => f₁ x - f₃ x) g

Defined in

Mathlib.Analysis.Asymptotics.Defs

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormSeminormedAddCommGroup