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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 928–964 (Mi izv1885)  

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

Conditional functions in the trajectory theory of dynamical systems

V. G. Vinokurov, N. N. Ganikhodzhaev


Abstract: In this paper the notion of a conditional function of a trajectory partition of a dynamical system is introduced. The properties of conditional functions are to a large extent analogous to those of a Rohlin system of conditional measures, which permits us to apply conditional functions to the study of nonmeasurable partitions, for which systems of conditional measures do not exist. With the aid of conditional functions a simple condition for measurability of a discrete partition is given, and a system of invariants for simple partitions of type II is constructed – a system analogous to the Rohlin system of invariants of a measurable partition.
Bibliography: 25 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 221–252

Bibliographic databases:

UDC: 519.53
MSC: 28D10
Received: 28.02.1977

Citation: V. G. Vinokurov, N. N. Ganikhodzhaev, “Conditional functions in the trajectory theory of dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 928–964; Math. USSR-Izv., 13:2 (1979), 221–252

Citation in format AMSBIB
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\by V.~G.~Vinokurov, N.~N.~Ganikhodzhaev
\paper Conditional functions in the trajectory theory of dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 928--964
\mathnet{http://mi.mathnet.ru/izv1885}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513908}
\zmath{https://zbmath.org/?q=an:0408.28018}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 221--252
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002041}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800002}


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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. L. Fëdorov, “Polymorphisms and partitions of Lebesgue spaces”, Funct. Anal. Appl., 16:2 (1982), 150–152  mathnet  crossref  mathscinet  zmath  isi
    2. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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