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Proceedings of the American Mathematical Society

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

 

 

Derivative measures


Authors: Casper Goffman and Fon Che Liu
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0550497-9
Keywords: Hausdorff measure, integral geometric measure, rectifiable
Article copyright: © Copyright 1980 American Mathematical Society