Some Elementary Properties ofKurzweil-Henstock-Stieltjes Integral on Rn

Kurzweil-Henstock integral is a generalization of the Reimann integral. In this paper, weestablished the definition of Kurzweil-Henstock-Stieltjes integral onRnvia gauge type approachwhere integrand and integrator are all real-valued functions defined on a compact interval inRn.Moreover, the Cauchy Criterion is established. To this end, some underlying simple propertiesof this integral are studied, specifically, uniqueness, linearity, monotonocity, integrability over asubset, and additivity. Results gathered in this paper may serve as a foundation to some relatedstudies such as the notion of convergence with respect to this integral, and the formulation ofthe Saks-Henstock Lemma.