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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

When total variation is additive


Author: F. S. Cater
Journal: Proc. Amer. Math. Soc. 84 (1982), 504-508
MSC: Primary 26A45; Secondary 26A30
MathSciNet review: 643738
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Abstract: Let $ f$ and $ g$ be continuous functions of bounded variation on $ [0,1]$. We use the Dini derivates of $ f$ and $ g$ to give a necessary and sufficient condition that the equation $ V(f + g) = V(f) + V(g)$ holds.


References [Enhancements On Off] (What's this?)

  • [1] Stanisław Saks, Theory of the integral, Second revised edition. English translation by L. C. Young. With two additional notes by Stefan Banach, Dover Publications, Inc., New York, 1964. MR 0167578 (29 #4850)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0643738-2
PII: S 0002-9939(1982)0643738-2
Keywords: Continuous function of bounded variation, total variation, absolutely continuous function, singular function, Lebesgue outer measure
Article copyright: © Copyright 1982 American Mathematical Society