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Avtomat. i Telemekh., 2007, Issue 11, Pages 208–222 (Mi at1087)  

This article is cited in 6 scientific papers (total in 6 papers)

Control of Systems

Construction of limiting process operations using ultrafilters of measurable spaces

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Consideration is given to representations of limiting process operations in terms of ultrafilters of measurable spaces and in terms of $(0,1)$-measures generated by these ultrafilters. Properties that are specified by the existence of non-Dirac countably additive $(0,1)$-measures and have the sense of degeneracy of corresponding “limiting” operations are studied. Properties of spaces whose elements are uniform limits of step mappings called tier mappings are analysed. We consider applications of these mappings in constructions connected with the design of correct extensions for abstract problems of attainability that admit natural analogs with problems of construction and study of properties of attainability domains of controlled systems.

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English version:
Automation and Remote Control, 2007, 68:11, 2083–2096

Bibliographic databases:

Document Type: Article
PACS: 02.30.Yy
Presented by the member of Editorial Board: A. I. Kibzun
Received: 14.12.2006

Citation: A. G. Chentsov, “Construction of limiting process operations using ultrafilters of measurable spaces”, Avtomat. i Telemekh., 2007, no. 11, 208–222; Autom. Remote Control, 68:11 (2007), 2083–2096

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Chentsov, “Prostranstvo stounovskogo predstavleniya i konstruktsii rasshirenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 2, 169–172  mathnet
    2. A. G. Chentsov, “On the result equivalence of constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S32–S53  mathnet  crossref  isi  elib
    3. Chentsov A.G., “Generalized limits and representations of attraction sets in problems with constraints of asymptotic character”, Doklady Mathematics, 85:1 (2012), 83–86  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. A. G. Chentsov, “Representation of attraction elements in abstract attainability problems with asymptotic constraints”, Russian Math. (Iz. VUZ), 56:10 (2012), 38–49  mathnet  crossref  mathscinet
    5. A. G. Chentsov, “Yarusnye otobrazheniya i preobrazovaniya na osnove ultrafiltrov”, Tr. IMM UrO RAN, 18, no. 4, 2012, 298–314  mathnet  elib
    6. A. G. Chentsov, “Ob odnom primere postroeniya mnozhestv prityazheniya s ispolzovaniem prostranstva Stouna”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 108–124  mathnet
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