Abstract
In this chapter we consider the necessary conditions for an extremum for optimization problems in a measure space. Let E be a space where besides linear and topological structures there is also a measure, i.e., some σ-algebra Σ of its subsets and a full measure μ on Σ are given in E [Hal, KA, KoF]. Here we assume that the topology in E is induced by some metric. Thus in this chapter the space E is a complete metrizable locally convex linear topological measure space (Fréchet space with measure μ).
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© 1998 Springer Science+Business Media Dordrecht
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Abramov, A.P. (1998). Necessary Conditions for an Extremum in a Measure Space. In: Connectedness and Necessary Conditions for an Extremum. Mathematics and Its Applications, vol 431. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9119-5_5
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DOI: https://doi.org/10.1007/978-94-015-9119-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4981-0
Online ISBN: 978-94-015-9119-5
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