Abstract:
Let (X,‖·‖) be a real separable Banach space with the dual X*, let (Ω,A,P) be a complete probability space, {Bn，n≤-1} be an increasing family of subfields of A. Firstly, some properties of random essential supremum are discussed, set-valued inverse superpramart approximation and set-valued inverse supermartingale convergence theorem in the sense of Kuratowski are provided, respectively. Lastly, set-valued inverse superpramart convergence theorem in the senses Kuratowski and Kuratowski-Mosco are proved, respectively.
