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Conditional expectation of weak random elements | ||
| Iranian Journal of Science | ||
| مقاله 5، دوره 36، شماره 4، بهمن 2012، صفحه 461-467 اصل مقاله (153.24 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2012.2107 | ||
| نویسندگان | ||
| S. Shishebor* 1؛ A. R. Soltani2؛ M. Sharifitabar3؛ Z. Sajjadnia1 | ||
| 1Department of Statistics, Shiraz University, Shiraz, Iran | ||
| 2Department of Statistics, Shiraz University (and Kuwait University) Shiraz, P.O. Box 5969 Safat 13060, Iran | ||
| 3School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran | ||
| چکیده | ||
| We prove that the limit of a sequence of Pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable Banach space is Pettis integrable. Then we provide basic properties for the Pettis conditional expectation, and prove that it is continuous. Calculus of Pettis conditional expectations in general is very different from the calculus of Bochner conditional expectations due to the lack of strong measurability and separability. In two examples, we derive the Pettis conditional expectations. | ||
| کلیدواژهها | ||
| Pettis integral؛ Pettis conditional expectation؛ non-separable Banach spaces؛ weak p-th order random elements | ||
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