The following containment theorem is presented: If
K and
L are convex bodies such that every simplex that contains
L also contains some translate of
K , then in fact the body
L must contain a translate of the body
K . One immediate consequence of this theorem is a strengthened version of Weil's mixed-volume characterization of containment.
Received October 31, 1995, and in revised form February 28, 1996.