Theorems · Theorem · functional analysis

Asymptotics.isLittleOTVS_pi

∀ {α : Type u_1} {𝕜 : Type u_3} {F : Type u_5} [inst : NontriviallyNormedField 𝕜] [inst_1 : AddCommGroup F]
  [inst_2 : TopologicalSpace F] [inst_3 : Module 𝕜 F] {l : Filter α} {g : α → F} {ι : Type u_7} {E : ι → Type u_8}
  [inst_4 : (i : ι) → AddCommGroup (E i)] [inst_5 : (i : ι) → Module 𝕜 (E i)]
  [inst_6 : (i : ι) → TopologicalSpace (E i)] [∀ (i : ι), ContinuousSMul 𝕜 (E i)] {f : α → (i : ι) → E i},
  f =o[𝕜; l] g ↔ ∀ (i : ι), (fun x => f x i) =o[𝕜; l] g

Defined in

Mathlib.Analysis.Asymptotics.TVS

Cited by

0 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupTopologicalSpaceModuleAddCommGroupModuleTopologicalSpaceContinuousSMul