Recently, based on the idea of randomizing space theory, random convex analysis has
been being developed in order to deal with the corresponding problems in random …

To provide a solid analytic foundation for the module approach to conditional risk measures,
our purpose is to establish a complete random convex analysis over random locally convex …

This paper constructs a counterexample showing that not every locally $ L^ 0$--convex
topology is necessarily induced by a family of $ L^ 0$--seminorms. Random convex analysis …

First, this paper introduces the notion of L 0-convex compactness for a special class of
closed convex subsets–closed L 0-convex subsets of a Hausdorff topological module over …

Several results in functional analysis are extended to the setting of $ L^ 0$-modules, where
$ L^ 0$ denotes the ring of all measurable functions $ x\colon\Omega\to\mathbb {R} $. The …

Motivated by the randomized version of the classical Bolzano–Weierstrass theorem, in this
paper we first introduce the notion of a random sequentially compact set in a random …

First, we prove that a random metric space can be isometrically embedded into a complete
random normed module, as an application it is easy to see that the notion of d-\(\sigma\) …

Locally L 0-convex modules were introduced in Filipovic et al.(2009)[10] as the analytic
basis for the study of conditional risk measures. Later, the algebra of conditional sets was …

Locally $ L^ 0$-convex modules were introduced in [D. Filipovic, M. Kupper, N. Vogelpoth.
Separation and duality in locally $ L^ 0$-convex modules. J. Funct. Anal. 256 (12), 3996 …

Based on conditional set theory, we study conditional weak topologies, extending some well-
known results to this framework and culminating with the proof of conditional versions of …