the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

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 c...

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.

Let μ and λ be two positive bounded measures on the same meaurable space (Ω,F). We call μ and λ equivalent, and write μ ≡ λ, if they have the same null sets— so, if they were probability measures, the notion of “a.s.” would be the same for both. More generally, we call λ absolutely continuous (AC) w.r.t. μ, and write λ μ, if μ(A) = 0 implies λ(A) = 0, i.e., if every μ-null set is also λ-null. W...