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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 13, Fasc. 1,
pages 71 - 76
 

SOME REMARKS ON MEASURES WITH n -DIMENSIONAL VERSIONS

J. K. Misiewicz

Abstract: A nondegenerate probability measure n on Rn is an n -dimensional version of a symmetric measure m on R if there exists c : Rn --> [0, oo ) such that ^n(ta) = ^m(|t| c(a)), t (- R, a (- Rn. If the function c is an L p -norm on Rn, we call the measure n p -elliptically contoured. The main result of this paper is that if m has an e -order for e > 0, then every its n -dimensional version is p -elliptically contoured for some p (- (0,2]. We show also that supp(m) = R if only m has an n -dimensional version which is not 2-elliptically contoured.

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

Key words and phrases: -

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