Approximation of Surface Measures in a Locally Convex Space

The main result of the paper is an analog of the surface layer theorem for measures given on a locally convex space with a continuously and densely embedded Hilbert subspace (for a surface of finite codimension). Earlier, the surface layer theorem was proved only for Banach spaces: for surfaces of codimension 1 by Uglanov (1979) and for surfaces of an arbitrary finite codimension by Yakhlakov (1990). In these works, the definition of the surface layer and the proof of the theorem essentially use the fact that the original space is equipped with a norm.