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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Derivative measures
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by Casper Goffman and Fon Che Liu PDF
Proc. Amer. Math. Soc. 78 (1980), 218-220 Request permission

Abstract:

A characterization of those measures which are distribution derivatives is undertaken. For functions of n variables in BVC, the derivative measures are absolutely continuous with respect to Hausdorff $n - 1$ measure. For functions in $W_1^1$ they are absolutely continuous with respect to n measure. For linearly continuous functions the derivative measures are zero for sets whose Hausdorff $n - 1$ measure is finite. For $n = 1$, since $n - 1 = 0$, this reduces to the standard facts.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 218-220
  • MSC: Primary 26B15; Secondary 26B30, 49F25
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0550497-9
  • MathSciNet review: 550497