For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, rando...For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.展开更多
基金Supported by the National Natural Science F oundation of China( No.10 0 710 5 8)
文摘For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.
