Laplace Transform of Constant Mapping

Theorem
Let $a \in \R$ be a real constant.

Let $f_a: \R \to \R$ or $\C$ be the constant mapping, defined as:
 * $\forall t \in \R: \map {f_a} t = a$

Let $\laptrans {f_a}$ be the Laplace transform of $f_a$.

Then:


 * $\laptrans {\map {f_a} t} = \dfrac a s$

for $\map \Re s > a$.