  The purpose of this note is to extend the $L^1$ averaging lemma of Golse and
Saint-Raymond \cite{GolSR} to the case of a kinetic transport equation with a
force field $F(x)\in W^{1,\infty}$. To this end, we will prove a local in time
mixing property for the transport equation $\partial_t f + v.\nabla_x f +
F.\nabla_v f =0$.
