Which measures are projections of purely unrectifiable one-dimensional Hausdorff measures
HTML articles powered by AMS MathViewer
- by Marianna Csörnyei and Ville Suomala PDF
- Proc. Amer. Math. Soc. 137 (2009), 145-154 Request permission
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
- K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
- 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, DOI 10.1017/CBO9780511623813
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
- MR Author ID: 759786
- Email: visuomal@maths.jyu.fi
- Received by editor(s): November 23, 2007
- Published electronically: August 13, 2008
- Communicated by: Tatiana Toro
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 145-154
- MSC (2000): Primary 28A78, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-08-09660-3
- MathSciNet review: 2439435