Let $M = (\mathbb{R}^N, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space such that

(i)	$f, g : \mathbb{R}^N \to \mathbb{C}$ are each an D5644: Absolutely integrable complex Borel function on $M$

Let $\alpha, \beta \in \mathbb{C}$ each be a D1207: Complex number.

Then \begin{equation} \mathfrak{F}_{\alpha f + \beta g} = \alpha \mathfrak{F}_f + \beta \mathfrak{F}_g \end{equation}