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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 6, Pages 1305–1323 (Mi izv2011)  

Quasi-invariant measures for topological dynamical systems

I. P. Kornfeld


Abstract: It is proved that for a topological dynamical system to admit an ergodic quasi-invariant measure of type III (a measure which is not equivalent to any $\sigma$-finite invariant measure) it is necessary and sufficient that this system have a recurrent point. For systems with a recurrent point, it is shown that there exist a nondenumerable number of pairwise singular ergodic quasi-invariant measures of type III.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:6, 1287–1304

Bibliographic databases:

UDC: 513.88
MSC: 28A65
Received: 20.06.1973

Citation: I. P. Kornfeld, “Quasi-invariant measures for topological dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974), 1305–1323; Math. USSR-Izv., 8:6 (1974), 1287–1304

Citation in format AMSBIB
\Bibitem{Kor74}
\by I.~P.~Kornfeld
\paper Quasi-invariant measures for topological dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 6
\pages 1305--1323
\mathnet{http://mi.mathnet.ru/izv2011}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=427590}
\zmath{https://zbmath.org/?q=an:0312.28021}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 6
\pages 1287--1304
\crossref{https://doi.org/10.1070/IM1974v008n06ABEH002148}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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