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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 jmzg1@um.es 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 [ Fulltext-pdf (149 KB)] for subscribers only. |