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Separation and duality in locally \(L^0\)-convex modules. (English) Zbl 1180.46055

The authors discuss the Hahn-Banach theorem and relevant convexity issues in the framework of a module over the ring of real measurable functions. The list of references reflects the previous research by the early 1980s. Some related results in a more general setting were obtained later by Boolean valued analysis and reflected, for instance, in [A.G.Kusraev and S.S.Kutateladze, “Subdifferential calculus.Theory and applications” (Russian) (Moskva:Nauka) (2007; Zbl 1137.49002)].

MSC:

46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
46N20 Applications of functional analysis to differential and integral equations
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Citations:

Zbl 1137.49002
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Full Text: DOI

References:

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