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

Author(s): Marianna Csörnyei; Ville Suomala
Journal: Proc. Amer. Math. Soc. 137 (2009), 145-154.
MSC (2000): Primary 28A78, 28A80
Posted: August 13, 2008
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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:

[Fa]
K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, Cambridge, 1986. MR 867284 (88d:28001)

[Ma]
P. Mattila, Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge University Press, Cambridge, 1995. MR 1333890 (96h:28006)

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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: 10.1090/S0002-9939-08-09660-3
PII: S 0002-9939(08)09660-3
Received by editor(s): November 23, 2007
Posted: August 13, 2008
Communicated by: Tatiana Toro
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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