Theorems · Theorem · integral transforms

isBigO_rpow_top_log_smul

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {f : ℝ → E},
  b < a → (f =O[Filter.atTop] fun x => x ^ (-a)) → (fun t => Real.log t • f t) =O[Filter.atTop] fun x => x ^ (-b)

If f is O(x ^ (-a)) as x → +∞, then log • f is O(x ^ (-b)) for every b < a.

Defined in

Mathlib.Analysis.MellinTransform

Cited by

1 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace