simpa [Real.fourierIntegral_def] using
  integral_add (integrable_fourierIntegrand f ξ) (integrable_fourierIntegrand g ξ)
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f g : 𝓢(ℝ, F)
ξ : ℝ
⊢ 𝓕 (fun x => f x + g x) ξ = 𝓕 (fun x => f x) ξ + 𝓕 (fun x => g x) ξ
no goals