The following theorem is proved: Let M be a locally Lipschitz hypersurface in C^n with one-sided extension property at each point (e.g., without analytic discs). Let S be a closed subset of M and f : M \ S ---> C^m \ E is a CR-mapping of class L^{ \infty} such that the cluster set of f on S along of Lebesque points of f is contained in a closed complete pluripolar set E. Then there is a CR-mapping \~f : M ---> C^m of class L^{ \infty}(M) such that \~f |M\S = f. It follows also that S is removable for CR \cap L^{ \infty} (M \ S).
Categories: math.CV