L^p-混合阵列加权和的L^r-收敛性和弱大数定律

L p -混合阵列加权和的L r -收敛性和弱大数定律 CONVERGENCE IN THE r th MEAN AND SOME WEAK LAWS OF LARGE NUMBERS FOR THE WEIGHTED SUMS OF L p MIXINGALE IN THE BANACH SPACE 刘京军 Liu Jingjun 1 first-author 甘师信 Gan Shixin 1 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 讨论了加权和∑ｌｎｉ＝１ａｎｉＸｎｉ的Ｌｒ－收敛性和弱大数定律，其中｛Ｘｎｉ，ｉ＝１，２，…，ｌｎ↑∞，ｎ≥１｝是Ｌｐ－混合阵列，｛ａｎｉ，ｉ＝１，２，…，ｌｎ↑∞，ｎ≥１｝是实数阵列． Let {X ni ,i=1,2,…,l n↑∞,n≥1}be an array of L p mixingale in Banach space B and let {a ni ,i=1,2,…l n↑∞,n≥1} be an array of real numbers.Some sufficient conditions of for weighted sums of convergence in probability and in r th  mean the form ∑ l n i=1 a ni X ni  are given.Some known results in this environment follow from our results. Lp－混合阵列 q阶光滑空间 弱大数定律 Lr－收敛性  p mixingale q smooth space weak laws of large numbers convergence in r th  mean O211.4 1998-01-01 2021-04-01 1