  The present note reviews some aspects of the mean field limit for Vlasov type
equations with Lipschitz continuous interaction kernel. We discuss in
particular the connection between the approach involving the N-particle
empirical measure and the formulation based on the BBGKY hierarchy. This leads
to a more direct proof of the quantitative estimates on the propagation of
chaos obtained on a more general class of interacting systems in [S.Mischler,
C. Mouhot, B. Wennberg, arXiv:1101.4727]. Our main result is a stability
estimate on the BBGKY hierarchy uniform in the number of particles, which
implies a stability estimate in the sense of the Monge-Kantorovich distance
with exponent 1 on the infinite mean field hierarchy. This last result
amplifies Spohn's uniqueness theorem [H. Spohn, Math. Meth. Appl. Sci. 3
(1981), 445-455].
