Slices of maps and Lebesgue area

Ziemer, William P.

doi:10.1090/S0002-9947-1972-0291415-0

Slices of maps and Lebesgue area
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by William P. Ziemer

Trans. Amer. Math. Soc. 164 (1972), 139-151

DOI: https://doi.org/10.1090/S0002-9947-1972-0291415-0

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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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