An interpolation property of locally Stein sets

We prove that, if D is a normal open subset of a Stein space X of pure
dimension such that D is locally Stein at every point of ∂D n Xsg, then, for every holomorphic vector bundle E over D and every discrete subset Ʌ of D \ Xsg whose set of accumulation points lies in ∂D \ Xsg, there is a holomorphic section of E over D with prescribed values on Ʌ. We apply this to the local Steinness problem and domains of holomorphy.