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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 1,
pages 215 - 222
 

COMPLETE EXACT LAWS

André Adler

Abstract: Consider independent and identically distributed random variables (X, X ,n > 1)
     n with xP (X > x)~  a(logx)a, where a > - 1 and P (X < -x)=  o(P(X > x)). Even though the mean does not exist, we establish Laws of Large Numbers of the form

 oo  sum     (|| sum n  akXk     ||   )
   cnP |--k=1----- -L |> e  <  oo 
n=1         bn
for all e > 0 and a particular nonsummable sequence (cn,n > 1), where L /= 0.

1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: Strong law of large numbers; weak law of large numbers; complete convergence.

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