Integration over Unbounded Multidimensional Intervals

In this paper we define an integral of Kurzweil]Henstock type over multidimensional unbounded intervals having the property that a multiple series converges in the sense of Hardy]M´oricz if and only if the associated step function is integrable in this sense. We show that this integral has good properties and in particular Hake’s property characterizing the integrability in terms of some convergence property of the associated indefinite integral, and a divergence theorem on unbounded intervals