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A new proof
of Federer's structure theorem
for $k$-dimensional subsets of $\mathbf{R}^{N}$


Author: Brian White
Journal: J. Amer. Math. Soc. 11 (1998), 693-701
MSC (1991): Primary 28A75, 28A78
DOI: https://doi.org/10.1090/S0894-0347-98-00267-7
MathSciNet review: 1603866
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that Federer's structure theorem for $k$-dimensional sets in $\mathbf{R}^{N}$ follows from the special case of $1$-dimensional sets in the plane, which was proved earlier by Besicovitch.


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

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  • [Fe1] H. Federer, The $(\phi ,k)$-rectifiable subsets of $n$ space, Trans. Amer. Math. Soc. 62 (1947), 114-192. MR 9:231c
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Additional Information

Brian White
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: white@math.stanford.edu

DOI: https://doi.org/10.1090/S0894-0347-98-00267-7
Received by editor(s): September 15, 1997
Received by editor(s) in revised form: February 12, 1998
Additional Notes: The author was partially funded by NSF grant DMS-95-04456.
Article copyright: © Copyright 1998 American Mathematical Society

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