The concepts of a conditional set, a conditional inclusion relation and a conditional
Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in …

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 …

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 …

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 …

In 1643 P. de Fermat introduced the problem of finding a point in the plane such that the sum
of its Euclidean distances to the three given points is minimal. Recently, Reich and Tuyen (J …

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 …

Our paper contributes to the theory of conditional risk measures and conditional certainty
equivalents. We adopt a random modular approach which proved to be effective in the study …

We study, for the first time in the literature on the theory of random functional analysis, the
Cauchy initial value problem in complete random normed modules. Under the L 0‐Lipschitz …