On a theorem of Fornaess and Narasimhan

We generalize a result of Fornoess and Narasimhan to the q-convex case, by showing that on every complex space X, each q-WPSH(X)-function which is con tinuous is also a q-PSH(X)-function (1 less than or equal to q) where q-WPS H(X) denotes the weakly q-plurisubharmonic functions and q-PSH(X) denotes t he q-plurisubharmonic functions on X. The idea of the proof is-based on ane w proof for the result of Fornoess and Narasimhan (i.e. for the case q = 1) . At the same time we obtain a generalization of a result of Siu, namely we show that every q-complete subspace with corners of a complex space admits a q-complete with corners neighborhood. (C) Academie des Sciences/Elsevier , Paris.