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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: 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?)

  • [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

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

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.

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