Geodesic
A characterization of the lattice group of Riemann integrable functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 3, pp. 101-140
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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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A. A. Seredinskii. A characterization of the lattice group of Riemann integrable functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 3, pp. 101-140. http://geodesic.mathdoc.fr/item/FPM_2006_12_3_a6/

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