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September 2021 On the multifractal analysis of measures in a probability space
Zhiming Li, Bilel Selmi
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Illinois J. Math. 65(3): 687-718 (September 2021). DOI: 10.1215/00192082-9446058

Abstract

In this paper, we calculate the relative multifractal Hausdorff and packing dimensions of measures in a probability space. Also, we obtain the analogue of Frostman’s lemma in a probability space for a relative multifractal Hausdorff measure. In the same way, there is a valid result for the relative multifractal packing pre-measure. Furthermore, we obtain the representations of the functions b and B by means of the analogue of Frostman’s lemma, and we provide a technique for showing that E is a (q,μ)-fractal with respect to ν. In addition, we suggest new proofs of theorems on the relative multifractal formalism in a probability space. They yield results even at a point q for which the multifractal functions b(q) and B(q) differ.

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Zhiming Li. Bilel Selmi. "On the multifractal analysis of measures in a probability space." Illinois J. Math. 65 (3) 687 - 718, September 2021. https://doi.org/10.1215/00192082-9446058

Information

Received: 6 January 2021; Revised: 16 July 2021; Published: September 2021
First available in Project Euclid: 31 August 2021

Digital Object Identifier: 10.1215/00192082-9446058

Subjects:
Primary: 28A78
Secondary: 28A80

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 3 • September 2021
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