  In 1972, E. P. Senkin generalized the celebrated theorem of A. V. Pogorelov
on unique determination of compact convex surfaces by their intrinsic metrics
in the Euclidean 3-space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$
under a mild assumption on the smoothness of the hypersurface. In this paper,
we remove this assumption and thus establish this rigidity result for arbitrary
compact, convex hypersurfaces in $E^{n+1}$, $n \ge 3$. We also prove the
corresponding results in other model spaces of constant curvature.
