The theory of theory of locally L^0-convex modules was introduced as the analytic basis for conditional L^0-convex risk measures. In this paper we first give some preliminaries of this theory and discuss about two kinds of countable concatenation properties. Second we extend to this framework some results from classical convex analysis , namely we provide randomized versions of Mazur lemma and Krein-\v{S .
We extend to the framework of locally L^0-convex modules some results from classical convex analysis . Namely, randomized versions of Mazur lemma and Krein-Smulian theorem under mild stability properties are provided .
R
The theory of theory of
We extend to the framework of
R
was introduced as the analytic basis for conditional L^0-convex risk measures. In this paper we first give some preliminaries of this theory and discuss about two kinds of countable concatenation properties. Second we extend to this framework some
some
R
, namely we provide
. Namely,
R
Krein-\v{S
Krein-Smulian theorem under mild stability properties are provided