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Outer Measures and Total Variation

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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In this note we collect some observations on the outer measures ψf and ψf that have been introduced in [4] and which describe the total variation of the function f. These properties have direct applications to the study of the derivative and the relative derivative. For definitions and notation the reader is referred to [4].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 3 , 01 September 1981 , pp. 341 - 345
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Bruckner, A. M., A note on measures determined by continuous functions, Canad. Math. Bull., (15. 2) (1972), 289-291.Google Scholar
2. Bruckner, A. M., Differentiation of real functions, Lecture Notes in Math. #659, Springer-Verlag (1978).Google Scholar
3. Henstock, R., The variation on the real line, Proc. Royal Irish Acad. 79A (1), 1-10.Google Scholar
4. Thomson, B. S., On the total variation of a function, Canad. Math. Bull.,Google Scholar
5. Saks, S., Theory of the Integral, Warsaw (1937).Google Scholar