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Partitioning Infinite‐Dimensional Spaces for Generalized Riemann Integration
Author(s) -
Henstock R.,
Muldowney P.,
Skvortsov V. A.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018819
Subject(s) - mathematics , cartesian product , simple (philosophy) , riemann sum , domain (mathematical analysis) , riemann hypothesis , pure mathematics , product (mathematics) , riemann integral , set (abstract data type) , mathematics subject classification , mathematical analysis , discrete mathematics , riemann problem , geometry , computer science , philosophy , epistemology , operator theory , fourier integral operator , programming language
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. 2000 Mathematics Subject Classification 28C20.