Linear Combination of Mellin Transforms

Theorem
Let $\MM$ be the Mellin transform.

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

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

Then:
 * $\map {\MM \set {\lambda \map f t + \map g t} } s = \lambda \map {\MM \set {\map f t} } s + \map {\MM \set {\map g t} } s$

everywhere all the above expressions are defined.