Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-30T19:29:14.274Z Has data issue: false hasContentIssue false
  • English
  • Français

A CONSTRUCTIVE LOOK AT FUNCTIONS OF BOUNDED VARIATION

Published online by Cambridge University Press:  01 May 2000

DOUGLAS S. BRIDGES
DOUGLAS S. BRIDGES
Affiliation:
Department of Mathematics & Statistics, University of Canterbury, Christchurch, New Zealand
Get access

Abstract

Functions with bounded variation and with a (total) variation are examined within Bishop's constructive mathematics. It is shown that the property of having a variation is hereditary downward on compact intervals, and hence that a real-valued function f with a variation on a compact interval can be expressed as a difference of two increasing functions. Moreover, if f is sequentially continuous, then the corresponding variation function, and hence f itself, is uniformly continuous.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 3 , May 2000 , pp. 316 - 324
Copyright
© The London Mathematical Society 2000

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.)