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An integral representation for a generalised variation of a function

Published online by Cambridge University Press:  17 April 2009

A.M. Russell
A.M. Russell
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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Abstract

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In this note we present sufficient conditions for the continuity of the total kth variation of a function defined on a closed interval [a, b]. We also give an integral representation for total feth variation, thus obtaining an extension of the classical result

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 2 , October 1974 , pp. 225 - 229
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Milne-Thomson, L.M., The calculus of finite differences (Macmillan & Co., London, 1933).Google Scholar
[2]Russell, A.M., “Functions of bounded kth variation”, Proc. London Math. Soc. (3) 26 (1973), 547–563.CrossRefGoogle Scholar