Theorems · Theorem · approximation theory

Asymptotics.isLittleO_iff_nat_mul_le_aux

∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {f : α → E} {g : α → F} {l : Filter α},
  ((∀ (x : α), 0 ≤ ‖f x‖) ∨ ∀ (x : α), 0 ≤ ‖g x‖) → (f =o[l] g ↔ ∀ (n : ℕ), ∀ᶠ (x : α) in l, ↑n * ‖f x‖ ≤ ‖g x‖)

Defined in

Mathlib.Analysis.Asymptotics.Defs

Cited by

3 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormNorm