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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
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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

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