  We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy
measure valued solutions of hyperbolic conservation laws. Sharp bounds for the
narrow convergence of MLMC for the entropy measure valued solutions are
proposed. An optimal work-vs-error bound for the MLMC method is derived
assuming only an abstract decay criterion on the variance. Finally, we display
numerical experiments of cases where MLMC is, and is not, efficient when
compared to Monte-Carlo.
