Theorems · Theorem · approximation theory

Asymptotics.IsLittleO.multisetProd

∀ {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 : Multiset ι} {f : ι → α → R} {g : ι → α → 𝕜},
  (∀ i ∈ s, f i =O[l] g i) →
    (∃ i ∈ s, f i =o[l] g i) →
      (fun x => (Multiset.map (fun x_1 => f x_1 x) s).prod) =o[l] fun x => (Multiset.map (fun x_1 => g x_1 x) s).prod

Defined in

Mathlib.Analysis.Asymptotics.Lemmas

Cited by

1 results in Mathlib

Foundations

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

Assumes

SeminormedCommRingNormedField