Henstock Type Integral for Vector Valued Functions in a Compact Metric Space

Abstract

We define a Henstock-type integral for vector valued functions defined in a probability metric compact Radon space, using a suitable family \({\mathcal B}\) of measurable sets which play the role of "intervals". When \({\mathcal B}\) is the family of all subintervals of \([0,1]\) we obtain the classical Henstock-Kurzweil integral on the real line, whereas if \({\mathcal B}\) is the family of all subintervals of \([0,1]^2\), or that of all subintervals of \([0,1]^2\) with a fixed regularity, we obtain the classical Henstock integral on the plane with respect to the Kurzweil base or the Kempisty base respectively.