Moment Complete Convergence for B-valued Martingale Random Variables

In this paper, the moment complete convergence for martingale random variables is discussed. Under certain moment condition, the moment complete convergence for B-valued martinagale random variables is obtained, and the result of Chow about the moment complete convergence for B-valued martingale random variables is generalized. The moment complete convergence for Martingale random variables is studied. Satisfactory results are obtained.