Theorems · Theorem · approximation theory

Asymptotics.IsBigO.finsetProd

∀ {α : Type u_1} {l : Filter α} {ι : Type u_17} {R : Type u_18} {𝕜 : Type u_19} [inst : SeminormedCommRing R]
  [inst_1 : NormedField 𝕜] {s : Finset ι} {f : ι → α → R} {g : ι → α → 𝕜},
  (∀ i ∈ s, f i =O[l] g i) → (fun x => ∏ i ∈ s, f i x) =O[l] fun x => ∏ i ∈ s, g i x

Defined in

Mathlib.Analysis.Asymptotics.Lemmas

Cited by

2 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedCommRingNormedField