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

Mean field limit for bosons and propagation of Wigner measures