  A convergence theorem for martingales with c\`adl\`ag trajectories (right
continuous with left limits everywhere) is obtained in the sense of the weak
dual topology on Hilbert space, under conditions that are much weaker than
those required for any of the usual Skorohod topologies. Examples are provided
to show that these conditions are also very easy to check and yield useful
asymptotic results, especially when the limit is a mixture of stochastic
processes with discontinuities.
