  We prove a local existence and uniqueness result for the non-relativistic and
relativistic Vlasov-Poisson system for data which need not even be continuous.
The corresponding solutions preserve all the standard conserved quantities and
are constant along their pointwise defined characteristic flow so that these
solutions are suitable for the stability analysis of not necessarily smooth
steady states. They satisfy the well-known continuation criterion and are
global in the non-relativistic case. The only unwanted requirement on the data
is that they be spherically symmetric.
