  We prove convergence of a class of space-time discontinuous Galerkin schemes
for scalar hyperbolic conservation laws. Convergence to the unique entropy
solution is shown for all orders of polynomial approximation, provided strictly
monotone flux functions and a suitable shock-capturing operator are used. The
main improvement, compared to previously published results of similar scope, is
that no streamline-diffusion stabilization is used. This is the way
discontinuous Galerkin schemes were originally proposed, and are most often
used in practice.
