A BOUNDARY UNIQUENESS THEOREM IN $ \mathbf{C}^n$

The classical boundary theorem of F. and M. Riesz asserts that, if the radial limits of a bounded holomorphic function in the disk lie in a set of capacity zero for a set of positive measure on the circle , then . The main result of this paper is the proof of an analogous theorem for maps , where is a domain in . We take as uniqueness set on the boundary any set of positive Lebesgue measure on a generating submanifold.Bibliography: 12 titles.

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