Mellin Transform of Heaviside Step Function/Lemma

Theorem
Let $t \in \R$.

Let $s \in \C$ with $\Re \left( s \right) < 0$.

Then:
 * $\displaystyle \lim_{t \to + \infty} t^s = 0$

Proof
Let $s=a+bi$, where $a, b \in \R$, $a<0$.