Non-zero boundaries of Leibniz half-spaces

Author:
Fuchang Gao

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1757-1762

MSC (2000):
Primary 46B20

DOI:
https://doi.org/10.1090/S0002-9939-04-07732-9

Published electronically:
November 19, 2004

MathSciNet review:
2120275

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Abstract: It is proved that for any , there exists a norm and two points , in such that the boundary of the Leibniz half-space has non-zero Lebesgue measure. When , it is known that the boundary must have zero Lebesgue measure.

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Additional Information

**Fuchang Gao**

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

DOI:
https://doi.org/10.1090/S0002-9939-04-07732-9

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

Published electronically:
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

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.