FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 3, PAGES 101-140

A characterization of the lattice group of Riemann integrable functions

A. A. Seredinskii

Abstract

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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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Last modified: July 22, 2006