Mellin Transform of Heaviside Step Function/Lemma

Theorem
Let $t \in \R$.

Let $s \in \C$ with $\map \Re s < 0$.

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

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