Theorems · Theorem · complex analysis

PhragmenLindelof.isBigO_sub_exp_exp

∀ {E : Type u_1} [inst : NormedAddCommGroup E] {a : ℝ} {f g : ℂ → E} {l : Filter ℂ} {u : ℂ → ℝ},
  (∃ c < a, ∃ B, f =O[l] fun z => Real.exp (B * Real.exp (c * |u z|))) →
    (∃ c < a, ∃ B, g =O[l] fun z => Real.exp (B * Real.exp (c * |u z|))) →
      ∃ c < a, ∃ B, (f - g) =O[l] fun z => Real.exp (B * Real.exp (c * |u z|))

An auxiliary lemma that combines two double exponential estimates into a similar estimate on the difference of the functions.

Defined in

Mathlib.Analysis.Complex.PhragmenLindelof

Cited by

2 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup