Theorems · Theorem · functional analysis

Asymptotics.IsLittleOTVS.exists_eventuallyLE_mul

∀ {𝕜 : Type u_1} {α : Type u_2} {E : Type u_3} {F : Type u_4} [inst : ENorm 𝕜] [inst_1 : TopologicalSpace E]
  [inst_2 : TopologicalSpace F] [inst_3 : Zero E] [inst_4 : Zero F] [inst_5 : SMul 𝕜 E] [inst_6 : SMul 𝕜 F]
  {l : Filter α} {f : α → E} {g : α → F},
  f =o[𝕜; l] g →
    ∀ U ∈ nhds 0, ∃ V ∈ nhds 0, ∀ (ε : NNReal), ε ≠ 0 → (fun x => egauge 𝕜 U (f x)) ≤ᶠ[l] fun x => ↑ε * egauge 𝕜 V (g x)

Defined in

Mathlib.Analysis.Asymptotics.TVS

Cited by

6 results in Mathlib

Foundations

Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENormTopologicalSpaceTopologicalSpaceZeroZeroSMulSMul