B值随机元阵列加权和的L^r收敛性

Convergence of Weighted Sums of Arrays of Banach Space Valued Elements

设B是实可分的Banach空间,{Xni,Fni,un≤i≤vn,n≥1}是B值适应随机元阵 列,{αni,un≤i≤un,n≥1}是实数阵列,当0<r<1或1≤r≤P且B是P可光滑时,研 究了∑i=un vn αniXni的Lr收敛性,所得的结果推广并改进了许多已知的结果.

Let B be a separable Banach space, let {Xni,Fni,un ≤i≤vn,n≤1} be an arrays of B-valued adapted random elements, and let {αni,un ≤ i ≤ vn,n ≥ 1} be an arrays of real numbers. When 0<r<1 or 1≤r≤p and B are p-smoothable, Lr convergence of weighted sums Σi=un vn αniXni is investigated in this paper. Some known results are extended.