  We present a generalized formulation of sweeping process where the behaviour
of the solution is prescribed at the jump points of the driving moving set. An
existence and uniqueness theorem for such formulation is proved. As a
consequence we derive a formulation and an existence/uniqueness theorem for
sweeping processes driven by an arbitrary BV moving set, whose evolution is not
necessarily right continuous. Applications to the play operator of
elastoplasticity are also shown.
