Integration over unbounded multidimensional intervals

Faure, CA.;Mawhin, Jean
(1997) Journal of Mathematical Analysis and Applications — Vol. 205, n° 1, p. 65-77 (1997)

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  • Faure, CA.
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  • Mawhin, JeanUCLouvain
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Abstract
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-Moricz 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. (C) 1997 Academic Press
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Faure, CA., & Mawhin, J. (1997). Integration over unbounded multidimensional intervals. Journal of Mathematical Analysis and Applications, 205(1), 65-77. https://doi.org/10.1006/jmaa.1996.5172 (Original work published 1997)