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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 thattrajectories may leave the state space $X$ and terminate. We introduce adiscrete infinitesimal generator and show, that the operator semigroupgenerated by this discrete generator converges in $L^1(X)$ pointwise to theFrobenius-Perron operator of the system.

Discrete infinitesimal generator of the Frobenius-Perron operator semigroup associated with "outflow systems"