Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) | $f, g : X \to \mathbb{C}$ are each a D5617: Complex Borel function on $M$ |
(ii) | \begin{equation} \int_X |f| \, d \mu, \int_X |g| \, d \mu < \infty \end{equation} |
(iii) | $\alpha, \beta \in \mathbb{C}$ are each a D1207: Complex number |
Then
\begin{equation}
\int_X (\alpha f + \beta g) \, d \mu
= \alpha \int_X f \, d \mu + \beta \int_X g \, d \mu
\end{equation}