Convergence results for a class of pramarts and superpramarts in Banach spaces

We prove several results in the convergence of vector-valued pramarts and convex weakly compact valued pramarts-sub-superpramarts in a separable Banach space. We also establish several a.s. norm convergence of vector-valued pramarts in the dual of a separable Banach space. An unusual convergence result for bounded positive vector-valued submartingales in separable order continuous Banach lattice is provided via a renorming lattice norm and other related tools.