The essential boundary of certain sets
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- by A. M. Bruckner, Roy O. Davies and C. Goffman
- Proc. Amer. Math. Soc. 96 (1986), 579-584
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826484-5
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Abstract:
The essential boundary of a measurable set is related to the de Giorgi perimeter and was introduced by Vol’pert in his "improvement" of Federer’s work. For a totally disconnected compact set of positive measure in $n$ space the essential boundary can be of Hausdorff $n - 1$ dimension but cannot have $\sigma$ finite $(n - 1)$-measure.References
- Herbert Federer, A note on the Gauss-Green theorem, Proc. Amer. Math. Soc. 9 (1958), 447–451. MR 95245, DOI 10.1090/S0002-9939-1958-0095245-2
- A. I. Vol′pert, Spaces $\textrm {BV}$ and quasilinear equations, Mat. Sb. (N.S.) 73 (115) (1967), 255–302 (Russian). MR 0216338
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 579-584
- MSC: Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826484-5
- MathSciNet review: 826484