Mathematical Sciences: Faculty Publications
Multifractal Structure of Noncompactly Supported Measures
Document Type
Article
Publication Date
9-2008
Publication Title
Fractals
DOI
10.1142/S0218348X0800396X
ISSN
1793-6543
Abstract
Many important definitions in the theory of multifractal measures on ℝd, such as the Lq-spectrum, L∞-dimensions, and the Hausdorff dimension of a measure, cannot be applied to non-compactly supported or infinite measures. We propose definitions that extend the original definitions to positive Borel measures on ℝd which are finite on bounded sets, and recover many important results that hold for compactly supported finite measures. In particular, we prove that if the Lq-spectrum is differentiable at q = 1, then the derivative is equal to the Hausdorff dimension of the measure.
Recommended Citation
Ngai, Sze-Man.
2008.
"Multifractal Structure of Noncompactly Supported Measures."
Fractals, 16 (3): 209-226.
doi: 10.1142/S0218348X0800396X
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/120
Copyright
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