When total variation is additive
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- by F. S. Cater PDF
- Proc. Amer. Math. Soc. 84 (1982), 504-508 Request permission
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
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 504-508
- MSC: Primary 26A45; Secondary 26A30
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643738-2
- MathSciNet review: 643738