Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A45, 26A30

Retrieve articles in all journals with MSC: 26A45, 26A30

Additional Information

Keywords: Continuous function of bounded variation, total variation, absolutely continuous function, singular function, Lebesgue outer measure
Article copyright: © Copyright 1982 American Mathematical Society