  We introduce a relaxation to the Aleksandrov relation assumption for the
Gauss Image Problem. This new assumption turns out to be a necessary condition
for two measures to be related by a convex body. We provide several properties
of the new condition. A solution to the Gauss Image Problem is obtained for the
case when one of the measures is assumed to be discrete and another measure is
assumed to be absolutely continuous, under the new relaxed assumption.
