Theorems · Theorem · functional analysis

Asymptotics.IsLittleOTVS.comp_tendsto

∀ {α : Type u_1} {β : Type u_2} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : AddCommGroup E] [inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] [inst_4 : AddCommGroup F]
  [inst_5 : TopologicalSpace F] [inst_6 : Module 𝕜 F] {l : Filter α} {f : α → E} {g : α → F} {k : β → α}
  {lb : Filter β}, f =o[𝕜; l] g → Filter.Tendsto k lb l → (f ∘ k) =o[𝕜; lb] (g ∘ k)

Defined in

Mathlib.Analysis.Asymptotics.TVS

Cited by

3 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupTopologicalSpaceModuleAddCommGroupTopologicalSpaceModule