Before revision:  Despite this, we will not only justify this mean-field limit (discrete in time) but will also show that the limit, as the discrete time interval \tau \to 0, approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system , in Wasserstein distance ; namely, the two limits \lim_{N\to\infty and \tau \to 0 commute} .
After revision:  Despite this, we will not only justify this mean-field limit (discrete in time) but will also show that the limit, as the discrete time interval \tau \to 0, approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system , in Wasserstein distance and \tau \to 0 commute} .