| Abstract: | For a sequence of constants {a
n,n 1}, an array of rowwise independent and stochastically dominated random elements { V
nj, j1, n1} in a real separable Rademacher type p (1 p2) Banach space, and a sequence of positive integer-valued random variables {T
n, n1}, a general weak law of large numbers of the form
![$$\sum {_{j = 1}^{T_n } } a_j (V_{nj} - c_{nj} )/b_{\alpha _n ]} \xrightarrow{P}0$$](/content/r52m6423xvu88287/10959_2004_Article_417604_TeX2GIFIE1.gif)
is established where {c
nj, j1, n1}, 
n   , b
n are suitable sequences. Some related results are also presented. No assumption is made concerning the existence of expected values or absolute moments of the {V
nj, j1, n1}. Illustrative examples include one wherein the strong law of large numbers fails. |
