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On the Total Variation of a Function

Published online by Cambridge University Press:  20 November 2018

B. S. Thomson
B. S. Thomson*
Affiliation:
Simon Fraser UniversityBritish Columbia, Canada
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There are a number of theories which assign to a function defined on the real line a measure that reflects somehow the variation of that function. The most familiar of these is, of course, the Lebesgue-Stieltjes measure associated with any monotonie function. The problem in general is to provide a construction of a measure from a completely arbitrary function in such a way that the values of this measure provide information about the total variation of the function over sets of real numbers and from which useful inferences can be drawn.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 3 , 01 September 1981 , pp. 331 - 340
Copyright
Copyright © Canadian Mathematical Society 1981

References

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