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

 

A doubling measure on $ \mathbb{R}^d$ can charge a rectifiable curve


Authors: John Garnett, Rowan Killip and Raanan Schul
Journal: Proc. Amer. Math. Soc. 138 (2010), 1673-1679
MSC (2010): Primary 28A75; Secondary 42B20
Published electronically: January 13, 2010
MathSciNet review: 2587452
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Abstract: For $ d\geq 2$, we construct a doubling measure $ \nu$ on $ \mathbb{R}^d$ and a rectifiable curve $ \Gamma$ such that $ \nu(\Gamma)>0$.


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Additional Information

John Garnett
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095

Rowan Killip
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095

Raanan Schul
Affiliation: Department of Mathematics, State University of New York, Stony Brook, New York 11794

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10234-2
PII: S 0002-9939(10)10234-2
Received by editor(s): June 14, 2009
Published electronically: January 13, 2010
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.