A random version of Mazur's lemma

2014/09/28 by José Miguel Zapata-García, Zapata-García, José Miguel
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Point processes and geometric inequalities #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1409.7932

openalex publication_date 2014/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to generalize the classical Mazur's lemma from the classical convex analysis to the framework of locally L⁰-convex modules. In this version an extra condition of countable concatenation is included. We provide a counterexample showing that this condition cannot be removed.

Citations

• On random convex analysis -- the analytic foundation of the module\n approach to conditional risk measures

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