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Mathematics of the USSR-Sbornik, 1976, Volume 29, Issue 2, Pages 217–222
DOI: https://doi.org/10.1070/SM1976v029n02ABEH003664
(Mi sm2777)
 

This article is cited in 3 scientific papers (total in 3 papers)

A result on differentiable measures on a linear space

A. V. Uglanov
References:
Abstract: The basic content of this note is the proof of the following result.
Let $X$ be a linear space, let $L$ be a subspace of it with $\dim L=m<\infty$, let $R$ be a ring of subsets of $X$ which is invariant with respect to shifts by vectors in $L$, and let $\sigma$ be a finitely additive bounded quasi-content on $R$ which is differentiable $n$ times with respect to the subspace $L$. Then, for any bounded set $W\subset L$,
$$ \lim_{r\to0}\sup_{L^c}\frac{|\sigma|(rW+L^c)}{r^{mn/(m+n)}}=0, $$
where $L^c$ is a linear complement to $L$ with respect to $X$, and $|\sigma|$ is the total variation of the quasi-content $\sigma$.
Bibliography: 2 titles.
Received: 07.03.1975
Bibliographic databases:
UDC: 513.88
MSC: Primary 28A15, 28A40; Secondary 28A10
Language: English
Original paper language: Russian
Citation: A. V. Uglanov, “A result on differentiable measures on a linear space”, Math. USSR-Sb., 29:2 (1976), 217–222
Citation in format AMSBIB
\Bibitem{Ugl76}
\by A.~V.~Uglanov
\paper A~result on differentiable measures on a~linear space
\jour Math. USSR-Sb.
\yr 1976
\vol 29
\issue 2
\pages 217--222
\mathnet{http://mi.mathnet.ru//eng/sm2777}
\crossref{https://doi.org/10.1070/SM1976v029n02ABEH003664}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=412371}
\zmath{https://zbmath.org/?q=an:0332.28005}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1976EZ91500007}
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  • https://doi.org/10.1070/SM1976v029n02ABEH003664
  • https://www.mathnet.ru/eng/sm/v142/i2/p242
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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