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Relations between some basic results derived from two kinds of topologies for a random locally convex module. (English) Zbl 1198.46058
The author discusses the Hahn--Banach theorem and relevant duality issues in the framework of a module over the ring of real measurable functions. More general results of the sort are readily available in [{\it S. S.\thinspace Kutateladze}, Sib. Math. J. 22, 575--583 (1982); translation from Sib. Mat. Zh. 22, 118--128 (1981; Zbl 0477.46017)]. The model-theoretic nature of convex analysis in modules was disclosed later within Boolean valued analysis; see, for instance, {\it E. I.\thinspace Gordon} [Sov. Math., Dokl. 23, 579--582 (1981); translation from Dokl. Akad. Nauk SSSR 258, 777--780 (1981; Zbl 0514.03032)], {\it A. G.\thinspace Kusraev} and {\it S. S.\thinspace Kutateladze} [“Introduction to Boolean-valued analysis” (Russian) (Moskva: Nauka) (2005; Zbl 1087.03032), “Subdifferential calculus. Theory and applications” (Russian) (Moskva: Nauka) (2007; Zbl 1137.49002)]. The author also addresses two types of completeness in the locally convex modules under consideration.

MSC:
46S50Functional analysis in probabilistic metric linear spaces
46H25Normed modules and Banach modules, topological modules
46A22Theorems of Hahn-Banach type; extension and lifting of functionals and operators
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Full Text: DOI
References:
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