  Suppose that metric measure spaces X_n=(X_n, d_n, m_n) satisfy RCD(K,infty)
conditions with m_n(X_n)=1. Then the measured Gromov convergence (introduced by
Gigili-Mondino-Savare '13) of X_n is equivalent to the weak convergence of the
laws of Brownian motions on X_n with initial distributions m_n.
