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Integration over Unbounded Multidimensional Intervals

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
205
Issue
1
Identifiers
DOI: 10.1006/jmaa.1996.5172
Disciplines
  • Mathematics

Abstract

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–Móricz 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.

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