Abstract
Let Omega be an open set in C-n, with n greater than or equal to 2 and let (X(k))(k) be a sequence of analytic sets of dimension p less than or equal to n - 2 in Omega. We prove that there exists a positive (1, 1)-current T on Omega such that the tangent cone of T does not exist at any point of boolean OR(k) X(k). More precisely we prove that for every open set omega subset of Omega and for every analytic set of dimension p less than or equal to n - 2 in Omega, there exists a closed positive current T of bidegree (1, 1) on Omega such that the tangent cone of T does not exist on X boolean AND omega and for every closed positive current Theta of bidegree (1, 1), the tangent cone of the current T + Theta does not exist at any point of X boolean AND omega.