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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 1, Fasc. 1,
pages 59 - 65
 

SOME REMARKS ON GAUSSIAN MEASURES IN BANACH SPACES

Stanisław Kwapień
Bogusław Szymański

Abstract: A sequence (x  )
  n of vectors in a Banach space E is called a representing sequence of a symmetric Gaussian measure m on E if there exists a sequence of independent Gaussian random variables (q )
  n such that  sum o o  x q
  n=1  n n  converges a.s. and m is its distribution. It is shown that for each symmetric Gaussian measure on E there exists a representing sequence (x )
 n such that  sum o o  ||x ||2
  n=1   n  is convergent. Also other results relating to representing sequences are established.

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

Key words and phrases: -

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