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Hausdorff and packing dimensions and sections of measures

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Maarit Järvenpää  and
Pertti Mattila
Maarit Järvenpää
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351, Jyväskylä, Finland.
Pertti Mattila
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351, Jyväskylä, Finland.
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Abstract

Let m and n be integers with 0<m<n and let μ be a Radon measure on ℝn with compact support. For the Hausdorff dimension, dimH, of sections of measures we have the following equality: for almost all (n − m)-dimensional linear subspaces V

provided that dimH μ > m. Here μv,a is the sliced measure and V⊥ is the orthogonal complement of V. If the (m + d)-energy of the measure μ is finite for some d>0, then for almost all (n − m)-dimensional linear subspaces V we have

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory

Information

Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 55 - 77
Copyright
Copyright © University College London 1998

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