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 partial derivative D \ X-sg, then, for every holomorphic vector bundle E over D and every discrete subset Lambda of D \ X-sg whose set of accumulation points lies in partial derivative D \ X-sg, there is a holomorphic section of E over D with prescribed values on Lambda. We apply this to the local Steinness problem and domains of holomorphy.