  We develop a general framework for the analysis of approximations to
stochastic scalar conservation laws. Our aim is to prove, under minimal
consistency properties and bounds, that such approximations are converging to
the solution to a stochastic scalar conservation law. The weak probabilistic
convergence mode is convergence in law, the most natural in this context. We
use also a kinetic formulation and martingale methods. Our result is applied to
the convergence of the Finite Volume Method in the companion paper [15].
