| Let (Ω,F,P) be a probability space,(Fn) be an increasing sequence of sub-σ-fields of F, a sequence (xn) of integrable random variables adapted to (Fn), if (xn) is progressive uniformly integrable or(xn)is a L1-bounded Semiamart, then ( 1 ) xm-xn→0 (Pr.), ( 2 ) E (xm|Fn)-xn→0 (pr.) are equivalent is proved in this paper . |
