Abstract

We extend to the framework of locally L0L^0-convex modules some results from the classical convex analysis. Namely, randomized versions of the Mazur lemma and the Krein-Šmulian theorem under mild stability properties are provided.

Author information

Contact details are reproduced from the original publication and may be historical.

José M. Zapata

Dpto. Matemáticas, Universidad de Murcia, 30100 Espinardo–Murcia, Spain

jmzg1@um.es

Keywords

  • Locally L0-convex module
  • stability properties
  • Mazur lemma
  • Krein-Šmulian theorem

Mathematics Subject Classification

46H25, 47H40, 52A41, 91B30, 91B70

Suggested citation

J. M. Zapata. “Randomized Versions of the Mazur Lemma and the Krein–Šmulian Theorem.” Journal of Convex Analysis 25 (2018), No. 3, 939–956. https://doi.org/10.68381/jca25061

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.