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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 407, Pages 7–16 (Mi znsl5483)  
On a comparison of Darboux and Riemann integrals in constructive analysis

A. A. Vladimirov

Dorodnitsyn Computing Center, Moscow, Russia
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Abstract: An example of constructive (in A. A. Markov's sense) real-valued function of one real variable which is integrable by Riemann, but is not integrable by Darboux, is constructed.
Key words and phrases: constructive function, Riemann integral, Darboux integral.
Received: 16.04.2012
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 199, Issue 1, Pages 1–5
DOI: https://doi.org/10.1007/s10958-014-1827-x
Bibliographic databases:
Document Type: Article
UDC: 510.25
Language: Russian
Citation: A. A. Vladimirov, “On a comparison of Darboux and Riemann integrals in constructive analysis”, Studies in constructive mathematics and mathematical logic. Part XII, Zap. Nauchn. Sem. POMI, 407, POMI, St. Petersburg, 2012, 7–16; J. Math. Sci. (N. Y.), 199:1 (2014), 1–5
Citation in format AMSBIB
\Bibitem{Vla12}
\by A.~A.~Vladimirov
\paper On a~comparison of Darboux and Riemann integrals in constructive analysis
\inbook Studies in constructive mathematics and mathematical logic. Part~XII
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 407
\pages 7--16
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5483}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3032181}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 1
\pages 1--5
\crossref{https://doi.org/10.1007/s10958-014-1827-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902247240}
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