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Proceedings of the American Mathematical Society

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Which measures are projections of purely unrectifiable one-dimensional Hausdorff measures


Authors: Marianna Csörnyei and Ville Suomala
Journal: Proc. Amer. Math. Soc. 137 (2009), 145-154
MSC (2000): Primary 28A78, 28A80
Published electronically: August 13, 2008
MathSciNet review: 2439435
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a necessary and sufficient condition for a measure $ \mu$ on the real line to be an orthogonal projection of $ \mathcal{H}^1_A$ for some purely $ 1$-unrectifiable planar set $ A$.


References [Enhancements On Off] (What's this?)

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  • [Ma] Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. Fractals and rectifiability. MR 1333890

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Additional Information

Marianna Csörnyei
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email: mari@math.ucl.ac.uk

Ville Suomala
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40014 Jyväskylä, Finland
Email: visuomal@maths.jyu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09660-3
Received by editor(s): November 23, 2007
Published electronically: August 13, 2008
Communicated by: Tatiana Toro
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.