SpringerIranian Journal of Science and Technology (Sciences)1028-627636420121107Conditional expectation of weak random elements461467210710.22099/ijsts.2012.2107ENS.ShisheborDepartment of Statistics, Shiraz University, Shiraz, IranA. R.SoltaniDepartment of Statistics, Shiraz University (and Kuwait University) Shiraz, P.O. Box 5969 Safat 13060, IranM.SharifitabarSchool of Mathematics, Institute for Research in Fundamental Sciences (IPM),
P.O. Box: 19395-5746, Tehran, IranZ.SajjadniaDepartment of Statistics, Shiraz University, Shiraz, IranJournal Article20111226We 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.http://ijsts.shirazu.ac.ir/article_2107_c87cfa778504a93d5a67510b8340c1fa.pdf