A generalization of the Levi problem with singularities

This result has been extended to open sets in Stein manifolds. But nothing is known about this if (Dj)j≥1 is a family of a Stein complex space X, even when X has isolated singularities. The main new result of this article concerns a generalization of this theorem for families of q-complete open sets in Stein spaces. By using a description of q-convex functions in terms of linear sets, introduced by M. Peternell [4], we show that if X is a Stein space and (Ω)j≥1 an increasing sequence of q-complete open subsets of X, then Ω = ⋃