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A Full Descriptive Definition of the Henstock–Kurzweil Integral in the Euclidean Space

Published online by Cambridge University Press:  23 October 2003

Lee Tuo-Yeong
Lee Tuo-Yeong
Affiliation:
Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Republic of Singapore. E-mail: tylee@nie.edu.sg
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Abstract

Using variational measures, we characterize additive interval functions which are indefinite Henstock–Kurzweil integrals in the Euclidean space, answering a problem posed by W. B. Jurkat and R. W. Knizia and independently by Lee Peng-Yee and Chew Tuan-Seng. This also extends a result of Bongiorno, Di Piazza and Skvortsov.

Keywords

Henstock variational measureHenstock–Kurzweil integralabsolute continuity28A1226B9926A39
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 3 , November 2003 , pp. 677 - 700
Copyright
2003 London Mathematical Society

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