Linear Combination of Mellin Transforms

Theorem
Let $\mathcal M$ be the Mellin transform.

Let $f \left({t}\right)$, $g \left({t}\right)$ be functions such that $\mathcal M \left\{ {f \left({t}\right)}\right\} \left({s}\right)$ and $\mathcal M \left\{ {f \left({t}\right)}\right\} \left({s}\right)$ exist.

Let $\lambda \in \C$ be a constant.

Then:
 * $\mathcal M \left\{ {\lambda f \left({t}\right) + g \left({t}\right)}\right\} \left({s}\right) = \lambda \mathcal M \left\{ {f \left({t}\right)}\right\}\left({s}\right) + \mathcal M \left\{ {g \left({t}\right)}\right\} \left({s}\right)$

everywhere all the above expressions are defined.