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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






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


Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 3, Pages 507–514 (Mi tvp647)  

Short Communications

A multidimensional analogue of Berry–Esseen's inequality for sets of a bounded diameter

V. M. Zolotarev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: In the space $R^n$ functions of hounded variation $L(x)$ and $H(x)$ are considered. Let $P_L$ and $P_H$ be the quasi-measures defined on Borel subsets of $R^n$ by the formulae
$$ P_L(B)=\int_B dL(x),\quad P_H(B)=\int_B dH(x). $$
Let us denote by $\mathfrak A_s$ the class of subsets of $R^n$ with the $(n-l)$-dimensional volumes of their boundaries not greater then $s$ and denote by $\mathfrak B_d$ the class of convex subsets of $R^n$ such that the $(n-l)$-dimensional volumes of their intersections with any hyperplane is not greater then $d$.
We construct an upper estimate (analogous to that of Berry–Esseen) of the quantity
$$ \Delta=\sup_{A\in\mathfrak G}|P_L(A)-P_H(A)| $$
where $\mathfrak G$ is $\mathfrak A_s$ or $\mathfrak B_d$.

Full text: PDF file (485 kB)

English version:
Theory of Probability and its Applications, 1966, 11:3, 447–454

Bibliographic databases:

Received: 16.05.1966

Citation: V. M. Zolotarev, “A multidimensional analogue of Berry–Esseen's inequality for sets of a bounded diameter”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 507–514; Theory Probab. Appl., 11:3 (1966), 447–454

Citation in format AMSBIB
\Bibitem{Zol66}
\by V.~M.~Zolotarev
\paper A~multidimensional analogue of Berry--Esseen's inequality for sets of a~bounded diameter
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 3
\pages 507--514
\mathnet{http://mi.mathnet.ru/tvp647}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=200959}
\zmath{https://zbmath.org/?q=an:0203.20102}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 3
\pages 447--454
\crossref{https://doi.org/10.1137/1111045}


Linking options:
  • http://mi.mathnet.ru/eng/tvp647
  • http://mi.mathnet.ru/eng/tvp/v11/i3/p507

    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
    Erratum
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:266
    Full text:97
    First page:4

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