MEAN CONVERGENCE THEOREMS AND WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACES

Title & Authors
MEAN CONVERGENCE THEOREMS AND WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACES
Dung, Le Van; Tien, Nguyen Duy;

Abstract
For a double array of random elements {$\small{V_{mn};m{\geq}1,\;n{\geq}1}$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which \$k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i
Keywords
martingale type p Banach spaces;double arrays of random elements;weighted double sums;weak laws of large numbers;mean convergence theorem;
Language
English
Cited by
1.
CONVERGENCE OF DOUBLE SERIES OF RANDOM ELEMENTS IN BANACH SPACES,;;

대한수학회지, 2012. vol.49. 5, pp.1053-1064
1.
A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers, Statistics & Probability Letters, 2012, 82, 1, 84
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