Theorems · Theorem · real analysis

Asymptotics.isTheta_const_smul_right

∀ {α : Type u_1} {E : Type u_3} {F' : Type u_7} {𝕜 : Type u_14} [inst : Norm E] [inst_1 : SeminormedAddCommGroup F']
  [inst_2 : NormedField 𝕜] {f : α → E} {g' : α → F'} {l : Filter α} [inst_3 : NormedSpace 𝕜 F'] {c : 𝕜},
  c ≠ 0 → ((f =Θ[l] fun x => c • g' x) ↔ 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