  In this technical report the $C_0$ semigroup of Frobenius-Perron operators on
$L^1(X)$ is considered, where the underlying dynamical system is such that
trajectories may leave the state space $X$ and terminate. We introduce a
discrete infinitesimal generator and show, that the operator semigroup
generated by this discrete generator converges in $L^1(X)$ pointwise to the
Frobenius-Perron operator of the system.
