  For the equations of elastodynamics with polyconvex stored energy, and some
related simpler systems, we define a notion of dissipative measure-valued
solution and show that such a solution agrees with a classical solution with
the same initial data when such a classical solution exists. As an application
of the method we give a short proof of strong convergence in the continuum
limit of a lattice approximation of one dimensional elastodynamics in the
presence of a classical solution. Also, for a system of conservation laws
endowed with a positive and convex entropy, we show that dissipative
measure-valued solutions attain their initial data in a strong sense after time
averaging.
