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

 

An estimate of the density at the boundary of an integral current modulo $ v$


Author: Sandra O. Paur
Journal: Proc. Amer. Math. Soc. 62 (1977), 319-322
MSC: Primary 58A25; Secondary 49F20
MathSciNet review: 0455005
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Abstract: An inequality is obtained which bounds the density at $ z \in {{\mathbf{R}}^n}$ of the boundary of a $ k + 1$ dimensional integral current modulo $ \nu \;{(S)^\nu }$ by the density of $ {(S)^\nu }$ at z. Also, the concept of boundary tangent developed in [3] is shown to be in agreement with Federer's concept of a measuretheoretic exterior normal if $ \nu = 0$ and S is obtained by integration over an $ {\mathfrak{L}^n}$ measurable subset of $ {{\mathbf{R}}^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0455005-9
PII: S 0002-9939(1977)0455005-9
Keywords: Integral current modulo $ \nu$, density, tangent, measuretheoretic exterior normal
Article copyright: © Copyright 1977 American Mathematical Society