  We prove a sufficient set of conditions for a sequence of finite measures on
the space of cadlag measure-valued paths to converge to the canonical measure
of super-Brownian motion in the sense of convergence of finite-dimensional
distributions. The conditions are convergence of the Fourier transform of the
$r$-point functions and perhaps convergence of the ``survival probabilities.''
These conditions have recently been shown to hold for a variety of statistical
mechanical models, including critical oriented percolation, the critical
contact process and lattice trees at criticality, all above their respective
critical dimensions.
