We extend a recent result of Avelin, Hed, and Persson about approximation of
functions f that are plurisubharmonic on a domain Ω and continuous on ˙Ω, with functions that are
plurisubharmonic on (shrinking) neighborhoods of ˙Ω. We show that such approximation is possible
if the boundary of Ω is C0 outside a countable exceptional set E⊂∂Ω. In particular, approximation
is possible on the Hartogs triangle. For Hölder 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 Hölder continuous case is possible.