  We consider the N-body Schr\"{o}dinger dynamics of bosons in the mean field
limit with a bounded pair-interaction potential. According to the previous work
\cite{AmNi}, the mean field limit is translated into a semiclassical problem
with a small parameter $\epsilon\to 0$, after introducing an
$\epsilon$-dependent bosonic quantization. The limit is expressed as a
push-forward by a nonlinear flow (e.g. Hartree) of the associated Wigner
measures. These object and their basic properties were introduced in
\cite{AmNi} in the infinite dimensional setting. The additional result
presented here states that the transport by the nonlinear flow holds for rather
general class of quantum states in their mean field limit.
