  In this paper, we consider the mean field limit of Brownian particles with
Coulomb interaction in 3D space. In particular, using a symmetrization
technique, we show that the limit measure almost surely is a weak solution to
the limiting nonlinear Fokker-Planck equation. By proving that the energy
almost surely is bounded by the initial energy, we improve the regularity of
the weak solutions. Moreover, by a natural assumption, we establish the weak
strong uniqueness principle, which is closely related to the propagation of
chaos.
