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Mat. Zametki, 1977, Volume 22, Issue 3, Pages 395–399 (Mi mz8060)  

Absolute upper semicontinuity

V. D. Ponomarev

Latvian State University

Abstract: It is proved that the following conditions are equivalent: the function $\varphi[a,b]\to R$ is absolutely upper semicontinuous (see [1]); $\varphi$ is a function of bounded variation with decreasing singular part; there exists a summable function $g:[a,b]\to R$ such that for any $t'\in[a,b]$ and $t"\in[t',b]$, we have $\varphi(t")-\varphi(t')\le\int_{t'}^{t"}g(s) ds$.

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English version:
Mathematical Notes, 1977, 22:3, 711–713

Bibliographic databases:

UDC: 517.9
Received: 05.03.1976

Citation: V. D. Ponomarev, “Absolute upper semicontinuity”, Mat. Zametki, 22:3 (1977), 395–399; Math. Notes, 22:3 (1977), 711–713

Citation in format AMSBIB
\Bibitem{Pon77}
\by V.~D.~Ponomarev
\paper Absolute upper semicontinuity
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 3
\pages 395--399
\mathnet{http://mi.mathnet.ru/mz8060}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=492467}
\zmath{https://zbmath.org/?q=an:0369.26006}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 3
\pages 711--713
\crossref{https://doi.org/10.1007/BF02412500}


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