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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v29.i1.30
pages 23-31

Relaxations of Attainable Sets and Their Generalized Representation in the Class of Two-Valued Finitely Additive Measures

Alexander G. Chentsov
N.N. Krasovsky Institute of Mathematics and Mechanics Ural Branch of Russian Academy of Sciences Ural Federal University Ekaterinburg, Russia
O. A. Cherepanova
Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences


The paper is aimed at constructing sets of asymptotic attainability in the space of functionals with the topology of pointwise convergence for the case where the constraints imposed on the choice of another system of functionals are perturbed. The construction of an extension in the class of two-valued normalized finitely additive measures is suggested for the case of embedding of the "conventional" solution space by assigning a Dirac measure to a selected point. The structure of the attraction set for the class of approximate solutions of the directedness type is established. The possibility for this set to be implemented in a "neighborhood" way as a "close" image set for the corresponding relaxation of the system of constraints is also established.

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