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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k063/k06307h.htm

Last modified: July 22, 2006