Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-29T21:20:04.224Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)