TY - JOUR ID - 2107 TI - Conditional expectation of weak random elements JO - Iranian Journal of Science JA - ISTT LA - en SN - 2731-8095 AU - Shishebor, S. AU - Soltani, A. R. AU - Sharifitabar, M. AU - Sajjadnia, Z. AD - Department of Statistics, Shiraz University, Shiraz, Iran AD - Department of Statistics, Shiraz University (and Kuwait University) Shiraz, P.O. Box 5969 Safat 13060, Iran AD - School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran Y1 - 2012 PY - 2012 VL - 36 IS - 4 SP - 461 EP - 467 KW - Pettis integral KW - Pettis conditional expectation KW - non-separable Banach spaces KW - weak p-th order random elements DO - 10.22099/ijsts.2012.2107 N2 - 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. UR - https://ijsts.shirazu.ac.ir/article_2107.html L1 - https://ijsts.shirazu.ac.ir/article_2107_c87cfa778504a93d5a67510b8340c1fa.pdf ER -