RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1978, Volume 105(147), Number 2, Pages 180–191 (Mi msb2524)  

This article is cited in 4 scientific papers (total in 4 papers)

Some properties of the normal image of convex functions

N. V. Krylov


Abstract: Let $z$ be a convex function defined in a convex domain $D$ of a finite-dimensional Euclidean space. Denote by $z^{(n)}$ the convolutions of $z$ with elements of a $\delta$-type sequence of test functions and let $\nu_z$ and $\nu_{z^{(n)}}$ be the measures of normal images corresponding to $z$ and $z^{(n)}$. One of the main results of this work is that $\nu_{z^{(n)}}\to\nu_z$ in variation on a compact $K\subset D$ if and only if $\nu_z$ is absolutely continuous on $K$ with respect to Lebesgue measure.
Bibliography: 7 titles.

Full text: PDF file (1032 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1978, 34:2, 161–171

Bibliographic databases:

UDC: 517.5
MSC: Primary 26A51, 28A20; Secondary 53C45
Received: 12.01.1977

Citation: N. V. Krylov, “Some properties of the normal image of convex functions”, Mat. Sb. (N.S.), 105(147):2 (1978), 180–191; Math. USSR-Sb., 34:2 (1978), 161–171

Citation in format AMSBIB
\Bibitem{Kry78}
\by N.~V.~Krylov
\paper Some properties of the normal image of convex functions
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 2
\pages 180--191
\mathnet{http://mi.mathnet.ru/msb2524}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=482157}
\zmath{https://zbmath.org/?q=an:0411.28008|0411.28009}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 2
\pages 161--171
\crossref{https://doi.org/10.1070/SM1978v034n02ABEH001154}


Linking options:
  • http://mi.mathnet.ru/eng/msb2524
  • http://mi.mathnet.ru/eng/msb/v147/i2/p180

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. N. V. Krylov, “On passing to the limit in degenerate Bellman equations. I”, Math. USSR-Sb., 34:6 (1978), 765–783  mathnet  crossref  mathscinet  zmath
    2. N. V. Krylov, “On passing to the limit in degenerate Bellman equations. II”, Math. USSR-Sb., 35:3 (1979), 351–362  mathnet  crossref  mathscinet  zmath  isi
    3. N. V. Krylov, “Some new results in the theory of controlled diffusion processes”, Math. USSR-Sb., 37:1 (1980), 133–149  mathnet  crossref  mathscinet  zmath  isi
    4. J. Spiliotis, “Certain results on a parabolic type Monge-Ampere equation”, Journal of Mathematical Analysis and Applications, 163:2 (1992), 484  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:227
    Full text:57
    References:37

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019