Convergence of uniformly Pettis integrable multivalued martingales. (English) Zbl 1516.60026
Summary: Some various convergence results are established for both uniformly Pettis integrable martingales with convex weakly compact values and Pettis integrable martingales with convex closed and bounded values in a separable Banach space. A Castaing representation of its Pettis integrable multivalued martingales is proved. Some properties of Pettis integrable multivalued functions are provided.
MSC:
| 60G42 | Martingales with discrete parameter |
| 28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
| 60B11 | Probability theory on linear topological spaces |
| 60B12 | Limit theorems for vector-valued random variables (infinite-dimensional case) |
| 60H05 | Stochastic integrals |
