Abstract
In this paper, we prove the existence of the trivial extension of S-plurisubharmonic currents of bidimension (p, p) defined outside an obstacle A of Hausdorff measure H-2p(A) = 0. Furthermore, a valid definition of the current dg boolean AND d(c) g boolean AND T is achieved for every positive closed current T and plurisubharmonic function g. The above results rely on an improvement of a classical result due to Demailly on the Monge-Ampere operator with a sharp condition on the Hausdorff measure. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.