STABLE AND SEMISTABLE PROBABILITY MEASURES ON CONVEX CONE

The study concerns semistability and stability of probability measures on a convex cone, showing that the set S (mu) of all positive numbers t > 0 such that a given probability measure mu is t-semistable establishes a closed subgroup of the multiplicative group R+; semistability and stability exponents of probability measures are positive numbers if and only if the neutral element of the convex cone coincides with the origin; a probability measure is (semi) stable if and only if its domain of (semi-) attraction is not empty; and the domain of attraction of a given stable probability measure coincides with its domain of semi-attraction.