A note on approximation of plurisubharmonic functions

We extend a recent result of Avelin, Hed, and Persson about approximation of functions f that are plurisubharmonic on a domain Omega and continuous on (Omega) over bar, with functions that are plurisubharmonic on (shrinking) neighborhoods of (Omega) over bar We show that such approximation is possible if the boundary of Omega is C-0 outside a countable exceptional set E subset of partial derivative Omega. In particular, approximation is possible on the Hartogs triangle. For Holder 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 Holder continuous case is possible.