Global weak solutions to the relativistic Vlasov-Maxwell system revisited

In 1989, R. DiPerna and P.-L. Lions established the existence of global weak solutions to the Vlasov-Maxwell system. In the present notes we give a somewhat simplified proof of this result for the relativistic version of this system, the main purpose being to make this important result of kinetic theory more easily accessible to newcomers in the field. We show that the weak solutions preserve the total charge.