In this correspondence, for a nonnegative regular summability matrix B and an array \(\left\{ a_{nk}\right\} \) of real numbers, the concept of B-statistical uniform integrability of a sequence of random variables \(\left\{ X_{k}\right\} \) with respect to \(\left\{ a_{nk}\right\} \) is introduced. This concept is more general and weaker than the concept of \(\left\{ X_{k}\right\} \) being uniformly integrable with respect to \(\left\{ a_{nk}\right\} \). Two characterizations of B-statistical uniform integrability with respect to \(\left\{ a_{nk}\right\} \) are established, one of which is a de La Vallée Poussin-type characterization. For a sequence of pairwise independent random variables \(\left\{ X_{k}\right\} \) which is B-statistically uniformly integrable with respect to \(\left\{ a_{nk}\right\} \), a law of large numbers with mean convergence in the statistical sense is presented for \(\sum \nolimits _{k=1}^{\infty }a_{nk}(X_{k}-\mathbb {E}X_{k})\) as \(n\rightarrow \infty \). A version is obtained without the pairwise independence assumption by strengthening other conditions.

在此对应关系中，对于非负正则求和矩阵B和实数数组\（\ left \ {a_ {nk} \ right \} \），B的概念-随机变量序列的统计统一可积\（相对于\（\ left \ {a_ {nk} \ right \} \）引入了\ left \ {X_ {k} \ right \} \）。该概念比\（\ left \ {X_ {k} \ right \} \）相对于\（\ left \ {a_ {nk} \ right \} \）可以统一集成的概念更为笼统和薄弱。关于\（\ left \ {a_ {nk} \ right \} \）B统计统一可积性的两个特征已建立，其中之一是de LaValléePoussin类型的特征。两两独立的随机变量的序列\（\左\ {X_ {K} \右\} \）是乙-statistically相对于均匀地积\（\左\ {A_ {NK} \右\} \），则针对\（\ sum \ nolimits _ {k = 1} ^ {\ infty} a_ {nk}（X_ {k}-\ mathbb {E} X_ { k}）\）为\（n \ rightarrow \ infty \）。通过加强其他条件，可以获得没有成对独立性假设的版本。