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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 3, Fasc. 2,
pages 155 - 171
 

A REPRESENTATION OF DISTRIBUTIONS
FROM CERTAIN CLASSES LidS

T. Rajba

Abstract: In this paper we define classes Lid S of certain infinitely divisible measures on the real line. We get a representation of the characteristic functions of distributions from certain classes Lid. S 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 Lid. S 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: -

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