  We extend a recent result of Avelin, Hed, and Persson about approximation of
functions $u$ that are plurisubharmonic on a domain $\Omega$ and continuous on
$\bar\Omega$, with functions that are plurisubharmonic on (shrinking)
neighborhoods of $\bar\Omega$. We show that such approximation is possible if
the boundary of $\Omega$ is $C^0$ outside a countable exceptional set
$E\subset\partial \Omega$. In particular, approximation is possible on the
Hartogs triangle. For H\"older continuous $u$, approximation is possible under
less restrictive conditions on $E$. We next give examples of domains where this
kind of approximation is not possible, even when approximation in the H\"older
continuous case is possible.
