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Fundam. Prikl. Mat., 2006, Volume 12, Issue 3, Pages 101–140 (Mi fpm953)  

A characterization of the lattice group of Riemann integrable functions

A. A. Seredinskii

M. V. Lomonosov Moscow State University

Abstract: In this paper, we give an algebraic characterization of the family of Riemann integrable functions in terms of lattice groups and a complete description of the Riemann extension of the lattice group of all continuous functions. We formulate a uniqueness theorem for the Riemann extension as a regular completion of the lattice group of all continuous functions.

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English version:
Journal of Mathematical Sciences (New York), 2008, 149:3, 1255–1278

Bibliographic databases:

UDC: 517.518.2+517.982.1+517.987.1

Citation: A. A. Seredinskii, “A characterization of the lattice group of Riemann integrable functions”, Fundam. Prikl. Mat., 12:3 (2006), 101–140; J. Math. Sci., 149:3 (2008), 1255–1278

Citation in format AMSBIB
\Bibitem{Ser06}
\by A.~A.~Seredinskii
\paper A~characterization of the lattice group of Riemann integrable functions
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 3
\pages 101--140
\mathnet{http://mi.mathnet.ru/fpm953}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249710}
\zmath{https://zbmath.org/?q=an:1146.26003}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 3
\pages 1255--1278
\crossref{https://doi.org/10.1007/s10958-008-0064-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-39049099463}


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  • Фундаментальная и прикладная математика
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