This is an announcement for the paper "On conditional weak topologies under a simplified approach derived the framework of conditional sets" by Jose Miguel Zapata.

Abstract: The purpose of this manuscript is to introduce a simplified approach derived from the framework of conditional sets, which is a novel approach to study dynamic and conditional settings, as those that arise in mathematical finance. Under this approach, and with the aim of providing an analytic basis for the study of dynamic and conditional risk measures, we carry out a study of the conditional weak topologies and conditional weak compactness, extending some well-known results to this framework and culminating with the proof of conditional versions of Eberlein-\v{S}mulian and Amir-Lindenstrauss Theorems. In pursuing this aim we study the algebraic structure of conditional spaces conditionally finitely generated and state conditional versions of Baire Category Theorem and Uniform Boundedness Principle.

Archive classification: math.FA

Submitted from: jmzg1@um.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1508.05112

or

http://arXiv.org/abs/1508.05112