Theorems · Theorem · approximation theory

Asymptotics.IsLittleO.mul_isBigO

∀ {α : Type u_1} {R : Type u_13} [inst : SeminormedRing R] {S : Type u_17} [inst_1 : NormedRing S] [NormMulClass S]
  {l : Filter α} {f₁ f₂ : α → R} {g₁ g₂ : α → S},
  f₁ =o[l] g₁ → f₂ =O[l] g₂ → (fun x => f₁ x * f₂ x) =o[l] fun x => g₁ x * g₂ x

Defined in

Mathlib.Analysis.Asymptotics.Defs

Cited by

11 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingNormedRingNormMulClass