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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
  • StanisÅ‚aw 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
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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