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Concerning the packing dimension of intersection measures

Published online by Cambridge University Press:  01 March 1997

MAARIT JÄRVENPÄÄ
MAARIT JÄRVENPÄÄ
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
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Abstract

For a Radon probability measure μ on ℝn we can use the Hausdorff dimension dimH and the packing dimension dimp to define lower indices

formula here

and

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For two such measures μ and ν intersection measures μ ∩ f# ν are obtained by slicing a certain product measure on ℝn × ℝn using diagonal n-planes, and by projecting the result onto ℝn. Here f is a similarity on ℝn and f# ν is the image of the measure ν under f. Our main result gives a lower bound for the packing dimension of these intersection measures under the condition dimH μ+dimH ν > n and some additional assumptions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 2 , March 1997 , pp. 287 - 296
Copyright
© Cambridge Philosophical Society 1997

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