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The essential boundary of certain sets

Authors: A. M. Bruckner, Roy O. Davies and C. Goffman
Journal: Proc. Amer. Math. Soc. 96 (1986), 579-584
MSC: Primary 28A75
MathSciNet review: 826484
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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 [Enhancements On Off] (What's this?)

  • [1] H. Federer, A note on the Gauss-Green theorem, Proc. Amer. Math. Soc. 9 (1958), 447-451. MR 0095245 (20:1751)
  • [2] A. I. Vol'pert, The spaces BV and quasilinear equations, Math. USSR-Sb. 2 (1967), 225-267. MR 0216338 (35:7172)

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Article copyright: © Copyright 1986 American Mathematical Society

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