Theorems · Theorem · functional analysis

Asymptotics.isThetaTVS_iff_isTheta

∀ {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : SeminormedAddCommGroup E] [inst_2 : SeminormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 E]
  [inst_4 : NormedSpace 𝕜 F] {f : α → E} {g : α → F} {l : Filter α}, f =Θ[𝕜; l] g ↔ f =Θ[l] g

Defined in

Mathlib.Analysis.Asymptotics.TVS

Cited by

2 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupSeminormedAddCommGroupNormedSpaceNormedSpace