MONGE-AMPERE OPERATOR AND SLICING FORMULA FOR A POSITIVE D-CLOSED CURRENT

Let U be the local potential of a positive d-closed current T of dimen sion p in an open subset Omega subset of C-n. Let v(1), ..., v(q) be p sh and bounded functions in Omega. We generalize some properties of th e current U boolean AND dd(c) v(1) boolean AND ... boolean AND dd(c) v (q) known when U is a psh function (p = n - 1) to the case of arbitrar y dimensions 0 < p < n. We prove some continuity properties of the Mon ge-Ampere operator with respect to non necessarily monotonic limits. W e also extend Federer's slicing formula and we prove that Federer's sl ices and Harvey's slices of T and U exist and they are equal outside a pluripolar subset. We give a necessary and suffisant condition for th e existence of the slice of U at a fixed point.