Published online by Cambridge University Press: 01 July 2016
Let , be i.i.d. random closed sets in
. Limit theorems for their normalized convex hulls
conv (
) are proved. The limiting distributions correspond to C-stable random sets. The random closed set A is called C-stable if, for any
, the sets anA and conv (
coincide in distribution for certain positive an, compact Kn, and independent copies A1, …, An of A. The distributions of C-stable sets are characterized via corresponding containment functionals.