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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Slices of maps and Lebesgue area


Author: William P. Ziemer
Journal: Trans. Amer. Math. Soc. 164 (1972), 139-151
MSC: Primary 28A75
MathSciNet review: 0291415
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Abstract: For a large class of k dimensional surfaces, S, it is shown that the Lebesgue area of S can be essentially expressed in terms of an integral of the $ k - 1$ area of a family, F, of $ k - 1$ dimensional surfaces that cover S. The family F is regarded as being composed of the slices of F. The definition of the $ k - 1$ area of a surface restricted to one of its slices is formulated in terms of the theory developed by H. Federer, [F3].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0291415-0
PII: S 0002-9947(1972)0291415-0
Keywords: Lebesgue area, slice of a surface, current valued measure, rectifiable set
Article copyright: © Copyright 1972 American Mathematical Society