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.
Citation
Caterina La Russa. "Henstock Type Integral for Vector Valued Functions in a Compact Metric Space." Real Anal. Exchange 36 (2) 435 - 448, 2010/2011.
Information