Covolution theorem for unilateral Laplace transform

Theorem

The following formula holds: $$\mathscr{L}_{\mathbb{T}}\{f*g\}(z)=\mathscr{L}\{f\}(z) \mathscr{L}\{g\}(z),$$ where $\mathscr{L}$ denotes the unilateral Laplace transform and $f*g$ denotes the unilateral convolution.