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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.


References [Enhancements On Off] (What's this?)

  • [1] H. Federer, Geometric measure theory, Springer, New York, 1969. MR 0257325 (41:1976)
  • [2] C. Goffman, A characterization of linearly continuous functions whose partial derivatives are measures, Acta Math. 117 (1967), 165-190. MR 0204584 (34:4423)
  • [3] C. Goffman and J. B. Serrin, Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964), 159-178. MR 0162902 (29:206)
  • [4] E. J. Mickie, On a decomposition theorem of Federer, Trans. Amer. Math. Soc. 92 (1959), 322-335. MR 0112947 (22:3792)

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Additional Information

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

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