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PARTITIONING INFINITE-DIMENSIONAL SPACES FOR GENERALIZED RIEMANN INTEGRATION

Published online by Cambridge University Press:  20 September 2006

R. HENSTOCK ,
P. MULDOWNEY  and
V. A. SKVORTSOV
R. HENSTOCK
Affiliation:
Department of Mathematics, University of Ulster, N. Ireland BT52 1SA
P. MULDOWNEY
Affiliation:
Magee College, University of Ulster, N. Ireland BT48 7JL p.muldowney@ulster.ac.uk
V. A. SKVORTSOV
Affiliation:
Department of Mathematics, Moscow State University, Moscow 119992, Russia and Akademia Bydgoska, 85-072 Bydgoszcz, Polandvaskvor2000@yahoo.com
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Abstract

To form Riemann sums for generalized Riemann integrals, the domain of integration must be partitioned in a suitable manner. The existence of the required partitions is usually proved by a simple method of repeated bisection of the domain of integration. However, when the domain is the Cartesian product of infinitely many copies of the set of real numbers, this simple method of proof has frequently failed. A proof which works for infinite-dimensional spaces is provided here.

Keywords

28C20
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 5 , October 2006 , pp. 795 - 803
Copyright
© The London Mathematical Society 2006

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