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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0826484-5
PII: S 0002-9939(1986)0826484-5
Article copyright: © Copyright 1986 American Mathematical Society