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Avtomat. i Telemekh., 2005, Issue 12, Pages 125–142 (Mi at1481)  

This article is cited in 2 scientific papers (total in 2 papers)

Deterministic Systems

Certain problems of asymptotic analysis and extensions. I

A. G. Chentsov

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

Abstract: Asymptotic attainability interpreted as the approximate realization of desirable states under weak slackening of constraints is studied. Constructs ensuring the realization of asymptotically attainable states in terms of standard constraints on the choice of generalized elements and interpreted as finitely additive measures on a suitable measurable space are designed. Special attention is paid to “Boolean-valued” realizations of generalized problems (extensions) in the class of (0,1)-measures or ultrafilters of measurable spaces and are interpreted as direct extension constructs (in the sense of transitions from exact solutions to approximate solutions).

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English version:
Automation and Remote Control, 2005, 66:12, 1983–1999

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: B. M. Miller
Received: 15.12.2002

Citation: A. G. Chentsov, “Certain problems of asymptotic analysis and extensions. I”, Avtomat. i Telemekh., 2005, no. 12, 125–142; Autom. Remote Control, 66:12 (2005), 1983–1999

Citation in format AMSBIB
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\by A.~G.~Chentsov
\paper Certain problems of asymptotic analysis and extensions.~I
\jour Avtomat. i Telemekh.
\yr 2005
\issue 12
\pages 125--142
\mathnet{http://mi.mathnet.ru/at1481}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2196468}
\zmath{https://zbmath.org/?q=an:1267.93018}
\elib{http://elibrary.ru/item.asp?id=16325479}
\transl
\jour Autom. Remote Control
\yr 2005
\vol 66
\issue 12
\pages 1983--1999
\crossref{https://doi.org/10.1007/s10513-005-0230-y}
\elib{http://elibrary.ru/item.asp?id=13481939}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-29144495782}


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  • http://mi.mathnet.ru/eng/at/y2005/i12/p125

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    This publication is cited in the following articles:
    1. A. G. Chentsov, “Certain problems of asymptotic analysis and extensions. II”, Autom. Remote Control, 67:1 (2006), 115–131  mathnet  crossref  mathscinet  zmath  elib  elib
    2. A. G. Chentsov, “Construction of limiting process operations using ultrafilters of measurable spaces”, Autom. Remote Control, 68:11 (2007), 2083–2096  mathnet  crossref  mathscinet  zmath  elib  elib
  • Avtomatika i Telemekhanika
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