Theorems · Theorem · real analysis

Asymptotics.isTheta_const_smul_left

∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} {𝕜 : Type u_14} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E']
  [inst_2 : NormedField 𝕜] {g : α → F} {f' : α → E'} {l : Filter α} [inst_3 : NormedSpace 𝕜 E'] {c : 𝕜},
  c ≠ 0 → ((fun x => c • f' x) =Θ[l] g ↔ f' =Θ[l] g)

Defined in

Mathlib.Analysis.Asymptotics.Theta

Cited by

3 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormSeminormedAddCommGroupNormedFieldNormedSpace