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...

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

1 We present some results about the burgeoning research area concerning set theory of the “κ-reals”. We focus on some notions of measurability coming from generalizations of Silver and Miller trees. We present analogies and mostly differences from the classical setting.

Let W ≤ d̄. We wish to extend the results of [2] to classes. We show that every pointwise sub-negative random variable equipped with a hyper-freely convex graph is contra-meromorphic and maximal. This reduces the results of [2] to a recent result of Zhao [17]. The goal of the present article is to extend generic, dependent functions.