Theorems · Theorem · functional analysis

Asymptotics.Filter.Tendsto.isBigOTVS_one

∀ {α : Type u_1} (𝕜 : Type u_3) {E : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] {l : Filter α} {f : α → E} [ContinuousAdd E] [ContinuousSMul 𝕜 E]
  {x : E}, Filter.Tendsto f l (nhds x) → f =O[𝕜; l] fun x => 1

If f converges along l to a finite limit x, then f =O[𝕜, l] 1.

Defined in

Mathlib.Analysis.Asymptotics.TVS

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldAddCommGroupTopologicalSpaceModuleContinuousAddContinuousSMul