Traces of functions belonging to Sobolev and Besov spaces and extensions from subsets of the Euclidean space

It is proved that from the existence of the trace operator, 0-dimensional Hausdorff measure in ⁿ and E is a Borel subset of ⁿ.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 137–145, 1987.