B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence (Journal of Mathematical Study, 2024)
In this paper, we first give the concept of B-statistical uniform integrabilitywith respect to Cesàro matrix (B-CUI), which is weaker than Cesàro uniform integrability. Then we establish some B-statistical convergence theorems for random sequenceunder the condition of B-CUI, which generalizes the outcomes of some known results.Finally, for some special kinds of triangular array or pairwise independent sequencesof random variables, similar results are also derived without conditions of B-CUI.
Keywords: B-statistical uniform integral; Cesàro matrix; martingale difference; $\mathfrak{L}_p$ convergence.