scholarly journals Strong Laws of Large Numbers for Weakly Orthogonal Sequences of Banach Space-Valued Random Variables

1974 ◽  
Vol 2 (5) ◽  
pp. 918-925 ◽  
Author(s):  
Anatole Beck ◽  
Peter Warren
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Orthogonal Sequences

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

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