Integration over unbounded multidimensional intervals (Q1353802)

The authors define and study a Kurzweil-Henstock type integral over multidimensional unbounded intervals such that the following holds true: A multiple series converges in the sense of Hardy-Móricz if and only if the associated step function is integrable in this sense. Among others, they prove that this integral enjoys the so-called Hake's property characterizing integrability in terms of some convergence property of the associated indefinite integral.