LIMIT-THEOREMS FOR CONVEX HULLS OF RANDOM SETS

Let A(n), n greater-than-or-equal-to 1, be i.i.d. random closed sets i n R(d). Limit theorems for their normalized convex hulls a(n)-1 conv ( A1 or...or A(n)) are proved. The limiting distributions correspond to C-stable random sets. The random closed set A is called C-stable if, f or any n greater-than-or-equal-to 2, the sets a(n)A and conv (A1 or... or A(n))+ K(n) coincide in distribution for certain positive a(n), com pact K(n), and independent copies A1,...,A(n) of A. The distributions of C-stable sets are characterized via corresponding containment funct ionals.