Affiliation: | Dipartimento di Matematica Pura ed Applicata ``G. Vitali', Università di Modena, via Campi 213/B, 41100 Modena, Italy ; Dipartimento di Statistica ``G. Parenti', Università di Firenze, viale Morgagni 59, 50134 Firenze, Italy |
Abstract: | Let be a vector lattice of real functions on a set with , and let be a linear positive functional on . Conditions are given which imply the representation , , for some bounded charge . As an application, for any bounded charge on a field , the dual of is shown to be isometrically isomorphic to a suitable space of bounded charges on . In addition, it is proved that, under one more assumption on , is the integral with respect to a -additive bounded charge. |