A characterization of the lattice group of Riemann integrable functions

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. © 2008 Springer Science+Business Media, Inc.