Filter.Eventually.isBigO

∀ {α : Type u_1} {E : Type u_3} [inst : Norm E] {f : α → E} {g : α → ℝ} {l : Filter α},
  (∀ᶠ (x : α) in l, ‖f x‖ ≤ g x) → f =O[l] g

See also Asymptotics.IsBigO.of_norm_eventuallyLE, which is the same lemma stated using Filter.EventuallyLE instead of Filter.Eventually.

Defined in: Mathlib.Analysis.Asymptotics.Defs
Cited by: 8 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Norm

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.