Some Fundamental Properties of Variational Kurzweil-Henstock-Stieltjes Integral on a Compact Interval in Rn

Abstract

Hoffman introduced the variational Kurzweil-Hentock-Stieltjes integral on a real-valued function and presented some of its properties. In this paper, we defined the variational Kurzweil-Henstock-Stieltjes integral on a compact interval in Rn. Fundamental properties such as uniqueness, linearity property and monotonocity property of both the integrand and integrator, additivity and integrability over a subinterval are provided. In addition, a characterization of the variational Kurzweil-Henstock-Stieltjes integral is established by formulating the Cauchy Criterion.