B-Statistical Uniform Integrability and $\mathfrak{L}_{p}$ Convergence

Abstract

In this paper, we first give the concept of B-statistical uniform integrability with respect to Cesaro matrix (B-CUI), which is weaker than Cesaro uniform integra-bility. Then we establish some B-statistical convergence theorems for random sequence under the condition of B-CUI, which generalizes the outcomes of some known results. Finally, for some special kinds of triangular array or pairwise independent sequences of random variables, similar results are also derived without conditions of B-CUI.

Keywords

B-statistical uniform integral / Cesaro matrix / martingale difference / $\mathfrak{L}_{p}$ convergence