• Kim, Tae-Sung (Mathematical Science Division, Wonkwang University) ;
  • Choi, Kyu-Hyuck (Mathematical Science Division, Wonkwang University) ;
  • Lee, Il-Hyun (Mathematical Science Division, Wonkwang University)
  • Published : 1999.05.01


In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.


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