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Upper conical density results for general measures on ℝn

Part of: Classical measure theory

Published online by Cambridge University Press:  30 April 2010

Marianna Csörnyei ,
Antti Käenmäki ,
Tapio Rajala  and
Ville Suomala
Marianna Csörnyei
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK (mari@math.ucl.ac.uk)
Antti Käenmäki
Affiliation:
Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland (antti.kaenmaki@jyu.fi; tapio.m.rajala@jyu.fi; ville.suomala@jyu.fi)
Tapio Rajala
Affiliation:
Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland (antti.kaenmaki@jyu.fi; tapio.m.rajala@jyu.fi; ville.suomala@jyu.fi)
Ville Suomala
Affiliation:
Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland (antti.kaenmaki@jyu.fi; tapio.m.rajala@jyu.fi; ville.suomala@jyu.fi)
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Abstract

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We study conical density properties of general Borel measures on Euclidean spaces. Our results are analogous to the previously known result on the upper density properties of Hausdorff and packing-type measures.

Keywords

upper conical densityHausdorff dimensionhomogeneity of measuresrectifiability

MSC classification

Secondary: 28A80: Fractals 28A75: Length, area, volume, other geometric measure theory 28A12: Contents, measures, outer measures, capacities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 311 - 331
Copyright
Copyright © Edinburgh Mathematical Society 2010