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.

UDC: 517.518.2+517.982.1+517.987.1

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

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