In this paper, we give an extension of Kronecker Lemma in Banach spaced B, and there by discuss the Lp convergence of the martingale transform Y=((?)Vk(Xk-Xk-1)Fn)n≥1,here X= (Xn,Fn)n≥0, is a B- valued L′ limit martingale and V = (Vn,Fn)n≥1 is a real-valued predictable sequence. |