Integrals on lattice-ordered groups
Ján Šípoš · Czech digital mathematics library · 1977
SIPOSThe notion of an upper integral was introduced for a real valued function by Bourbaki [2] and Topsoe [6].Integrability with respect to an upper integral was introduced there as well.These methods resemble the measurability of sets with respect to an outer measure.Neither Bourbaki's nor Topsoe's definition of an upper integral is axiomatic.Both utilize the properties which follow from the special methods of constructing the integral.The aim of this paper is to introduce the notion of integrability which will be defined axiomatically.The family of all real functions on any space is an 1-group.So we shall build up an integration theory on an 1-group. IntegrationWe shall be concerned below with lattice ordered groups, or 1-groups, in the following sense.