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Local dimensions of sliced measures and stability of packing dimensions of sections of sets
Authors:Esa Järvenpää  Maarit Järvenpää
Institution:a Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40014, Finland
b Friedrich-Schiller-Universität Jena, Mathematisches Institut, D-07740 Jena, Germany
Abstract:Let m and n be integers with 0<m<n. We relate the absolutely continuous and singular parts of a measure μ on View the MathML source to certain properties of plane sections of μ. This leads us to prove, among other things, that the lower local dimension of (nm)-plane sections of μ is typically constant provided that the Hausdorff dimension of μ is greater than m. The analogous result holds for the upper local dimension if μ has finite t-energy for some t>m. We also give a sufficient condition for stability of packing dimensions of section of sets.
Keywords:28A78  28A80
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