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Partitioning Infinite-Dimensional Spaces for Generalized Riemann Integration |
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| Authors: | Henstock R; Muldowney P; Skvortsov V A |
| Institution: | Department of Mathematics, University of Ulster N. Ireland BT52 1SA Magee College, University of Ulster N. Ireland BT48 7JL p.muldowney{at}ulster.ac.uk Department of Mathematics, Moscow State University Moscow 119992, Russia and Akademia Bydgoska 85-072 Bydgoszcz, Poland vaskvor2000{at}yahoo.com |
| Abstract: | To form Riemann sums for generalized Riemann integrals, thedomain of integration must be partitioned in a suitable manner.The existence of the required partitions is usually proved bya simple method of repeated bisection of the domain of integration.However, when the domain is the Cartesian product of infinitelymany copies of the set of real numbers, this simple method ofproof has frequently failed. A proof which works for infinite-dimensionalspaces is provided here. 2000 Mathematics Subject Classification28C20. |
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