CONVERGENCE OF MARTINGALE-LIKE SEQUENCES IN BANACH LATTICES WITHOUT （RNP）

In this paper it is proved that （1） under the supposition E is an order continuous Banach lattice and$\left(x_n, \mathscr{F}_n\right)_{n>1}$ is a subpramart of class （C）, if there is an a. e. strongly convergent and strongly measurable sequence （y_n）_n≥1 such that 0≤x_n≤y_n, n≥1, then （x_n）_n≥1 is a. e. strongly convergent, and every E⁺-valued reversed subpramart is a. e. strongly convergent; （2） under the supposition E is an AL space, if $\left(x_n, \mathscr{F}_n\right)_{n>1}$ is an E⁺- valued superpramart, then TL x_n a. e. exists.