On B-statistical uniform nonintegrability of a sequence of random variables

Mengru Chen, Guangying Li, Zhongzhi Wang, Yongjin Zhang

In this paper, we introduce a notion of B-statistical uniform nonintegrability with respect to A (B-UNI(c) w.r.t. A, in short), which is weaker than UNI(c) w.r.t. A (see [3]). We establish the de La Vall´ee Poussin criterion for B-UNI(c) w.r.t. A, which extends Theorem 2.1 of Chandra et al. (2021) [3]. Moreover, we also give a necessary condition for the sequence of random variables {Xk, k ∈ N} to be B-UNI(c) w.r.t. A.