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
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- Casper Goffman, A characterization of linearly continuous functions whose partial derivatives are measures, Acta Math. 117 (1967), 165–190. MR 204584, DOI 10.1007/BF02395044
- Casper Goffman and James Serrin, Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964), 159–178. MR 162902
- Earl J. Mickle, On a decompostion theorem of Federer, Trans. Amer. Math. Soc. 92 (1959), 322–335. MR 112947, DOI 10.1090/S0002-9947-1959-0112947-5
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