Approximation of Pettis integrable multifunctions with values in arbitrary Banach spaces. (English) Zbl 1284.28006
Pettis (and also Gelfand and Dunford) integrable multifunctions with bounded, closed and convex values in non-separable Banach spaces, defined on a complete probability space, are exhaustively investigated. Possible approximations by a (martingale) sequence of simple multiplication in various metrics are characterized. Then a multivalued version of the strong law of large numbers is treated.
Reviewer: Wlodzimierz Ślȩzak (Bydgoszcz)
MSC:
28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
54C60 | Set-valued maps in general topology |
60F15 | Strong limit theorems |
26E25 | Set-valued functions |
46G10 | Vector-valued measures and integration |
54C65 | Selections in general topology |