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Multifractal dimensions of product measures

Published online by Cambridge University Press:  24 October 2008

L. Olsen
L. Olsen
Affiliation:
University of St. Andrews, Department of Mathematics, North Haugh, St. Andrews, Fife KY16 9SS, Scotland e-mail: lo@st-and.ac.uk
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Abstract

We study the multifractal structure of product measures. for a Borel probability measure μ and q, t Є , let and denote the multifractal Hausdorff measure and the multifractal packing measure introduced in [O11] Let μ be a Borel probability merasure on k and let v be a Borel probability measure on t. Fix q, s, t Є . We prove that there exists a number c > 0 such that for E ⊆k, F ⊆l and Hk+l provided that μ and ν satisfy the so-called Federer condition.

Using these inequalities we give upper and lower bounds for the multifractal spectrum of μ × ν in terms of the multifractal spectra of μ and ν

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 4 , November 1996 , pp. 709 - 734
Copyright
Copyright © Cambridge Philosophical Society 1996

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