A random version of Mazur's lemma

Abstract

The purpose of this paper is to generalize the classical Mazur's lemma from the classical convex analysis to the framework of locally $L^0$-convex modules. In this version an extra condition of countable concatenation is included. We provide a counterexample showing that this condition cannot be removed.

References in corpus (3)

• Recent progress in random metric theory and its applications to conditional risk measures
• On random convex analysis -- the analytic foundation of the module approach to conditional risk measures
• On characterization of locally $L^0$-convex topologies induced by a family of $L^0$-seminorms

Cited by in corpus (3)

• The algebra of conditional sets and the concepts of conditional topology and compactness
• Versions of Eberlein-Šmulian and Amir-Lindenstrauss theorems in the framework of conditional sets
• A study of stability in locally $L^0$-convex modules and a conditional version of James' compactness theorem