$\underset{s\to {0}^{+}}{lim}{\int}_{0}^{\mathrm{\infty}}a(t){e}^{-st}dt$

${\int}_{0}^{\mathrm{\infty}}a(t){e}^{-st}dt=f(s)$

What is the meaning of the limit of this integral as $s\to {0}^{+}.$

${\int}_{0}^{\mathrm{\infty}}a(t){e}^{-st}dt=f(s)$

What is the meaning of the limit of this integral as $s\to {0}^{+}.$