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 | References | Similar Articles | Additional Information

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 measure. For functions in they are absolutely continuous with respect to *n* measure. For linearly continuous functions the derivative measures are zero for sets whose Hausdorff measure is finite. For , since , this reduces to the standard facts.

**[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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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