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Non-zero boundaries of Leibniz half-spaces

Author(s): Fuchang Gao
Journal: Proc. Amer. Math. Soc. 133 (2005), 1757-1762.
MSC (2000): Primary 46B20
Posted: November 19, 2004
MathSciNet review: 2120275
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Abstract: It is proved that for any $d\geq 3$ , there exists a norm $\Vert\cdot\Vert$ and two points , in $\mathbb{R}^d$ such that the boundary of the Leibniz half-space $H(a,b)=\{x\in \mathbb{R}^d: \Vert x-a\Vert\leq\Vert x-b\Vert\}$ has non-zero Lebesgue measure. When , it is known that the boundary must have zero Lebesgue measure.

References:

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Additional Information:

Fuchang Gao
Affiliation: Department of Mathematics, University of Idaho, Moscow, Idaho 83843

DOI: 10.1090/S0002-9939-04-07732-9
PII: S 0002-9939(04)07732-9
Keywords: Leibniz half-space, Voronoi region, metric entropy
Received by editor(s): August 26, 2003
Received by editor(s) in revised form: February 17, 2004
Posted: November 19, 2004
Additional Notes: This research was partially supported by NSF grant EPS-0132626 and a seed grant from the University of Idaho.
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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