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Journal of Convex Analysis 25 (2018), No. 3, 939--956
Copyright Heldermann Verlag 2018

Randomized Versions of the Mazur Lemma and the Krein–Smulian Theorem

José M. Zapata
Dpto. Matemáticas, Universidad de Murcia, 30100 Espinardo--Murcia, Spain

We extend to the framework of locally L0-convex modules some results from the classical convex analysis. Namely, randomized versions of the Mazur lemma and the Krein-Smulian theorem under mild stability properties are provided.

Keywords: Locally L0-convex module, stability properties, Mazur lemma, Krein-Smulian theorem.

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

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