Multidimensional Differential Calculus in Riesz spaces

ABSTRACT. Some versions of the divergence theorem are proved, for maps defined in suitable sets of IRn and with values in a Dedekind complete Riesz space R. Some applications to exact linear differential forms are given. 1 Introduction. In the literature there are many studies about Henstock-Kurzweil and Kurzweil-Stieltjes-type integrals for mappings, defined in a suitable subset of IR and taking values in Riesz spaces. Among the Authors, we recall Duchoň, Riečan and Vrábelova ́ (see [4], [24], [25] and its very rich bibliography, [26], [27], [28]), and the references quoted in [2]