Abstract. We study the question of when a γ-plurisubharmonic function on a complex manifold, where γ is a fixed (1, 1)-form, can be approximated by a decreasing sequence of smooth γ-plurisubharmonic functions. We show in particular that it is always possible in the compact Kähler case.
We give a precise characterization of those plurisubharmonic functions for which one can well define the Monge-Ampère operator as a regular Borel measure.
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