A REPRESENTATION OF DISTRIBUTIONS

FROM CERTAIN CLASSES

Abstract: In this paper we define classes of certain infinitely divisible measures on the
real line. We get a representation of the characteristic functions of distributions from
certain classes The method of our proof, stimulated by results of Urbanik [5]
consists in finding the extreme points of a certain convex set formed by Khintchine
measures of distributions from Once the extreme points are found, one can
apply Choquet’s theorem on representation of the points of a compact convex set as
barycenters of the extreme points ([4], p. 19). From Choquet’s uniqueness theorem
for a metrizable space X we obtain the uniqueness of representation ([41], p. 70).

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -