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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 5, Pages 1114–1134 (Mi izv1438)  

This article is cited in 1 scientific paper (total in 1 paper)

On a sufficient condition for integrability of the banach indicatrix of a smooth mapping

S. A. Gulevich


Abstract: Sufficient conditions are given for the convergence of integrals of the form $\int_{\mathbf R^k}(N(f,y))^p dy$, where $f\colon\mathbf R^n\to\mathbf R^k$ is a map with compact support with $k\leqslant n$ and $N(f,y)$ is the number of connected components of the level set $\{x:f(x)=y\}$.
Bibliography: 5 titles.

Full text: PDF file (1850 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:2, 391–408

Bibliographic databases:

UDC: 513.88
MSC: Primary 55M25; Secondary 26A39, 26B15, 28A75, 58C25, 58G10
Received: 21.04.1982

Citation: S. A. Gulevich, “On a sufficient condition for integrability of the banach indicatrix of a smooth mapping”, Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983), 1114–1134; Math. USSR-Izv., 23:2 (1984), 391–408

Citation in format AMSBIB
\Bibitem{Gul83}
\by S.~A.~Gulevich
\paper On a~sufficient condition for integrability of the banach indicatrix of a~smooth mapping
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 5
\pages 1114--1134
\mathnet{http://mi.mathnet.ru/izv1438}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=718418}
\zmath{https://zbmath.org/?q=an:0558.47047|0543.47052}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 2
\pages 391--408
\crossref{https://doi.org/10.1070/IM1984v023n02ABEH001776}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Gulevich, “On integrability of the Banach indicatrix of a smooth mapping”, Math. USSR-Izv., 25:1 (1985), 19–44  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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