  We show that the non-centered maximal function of a BV function is
quasicontinuous. We also show that \emph{if} the non-centered maximal functions
of an SBV function is a BV function, then it is in fact a Sobolev function.
Using a recent result of Weigt, we are in particular able to show that the
non-centered maximal function of a set of finite perimeter is a Sobolev
function.
