This paper is concerned with lattice-group valued measures for which the sygma-additivity is defined by means of the order convergence properties. In the first section we treat the analogues for such order-measures with values in a Dedekind complete lattice-group of the Jordan, Lebesgue and Yosida-Hewitt descompositions. The second section deals with the construction of an integral for functions with respect to an order-measure, both taking their values in a Dedekind sygma-complete lattice-ring. Analogues of the monotone-convergence, dominated-convergence and Fatou theorems are obtained.
@article{urn:eudml:doc:38852,
title = {Medidas y probabilidades en estructuras ordenadas.},
journal = {Stochastica},
volume = {5},
year = {1981},
pages = {45-68},
zbl = {0478.28008},
mrnumber = {MR0659246},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38852}
}
Congost Iglesias, María. Medidas y probabilidades en estructuras ordenadas.. Stochastica, Tome 5 (1981) pp. 45-68. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38852/