Definition:Convolution Integral/Positive Real Domain

Definition
Let $f$ and $g$ be functions which are integrable. Let $f$ and $g$ be supported on the positive real numbers $\R_{\ge 0}$ only.

The convolution integral of $f$ and $g$ may be defined as:
 * $\displaystyle \map f t * \map g t = \int_0^t \map f u \map g {t - u} \rd u$