On the mutual singularity of multifractal measures

Zied Douzi; Bilel Selmi; Zied Douzi; Bilel Selmi

doi:10.3934/era.2020024

Electronic Research Archive

2020, Volume 28, Issue 1: 423-432. doi: 10.3934/era.2020024

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On the mutual singularity of multifractal measures

Zied Douzi ^,,
Bilel Selmi

Analysis, Probability and Fractals Laboratory LR18ES17, Faculty of Sciences of Monastir, Department of Mathematics, 5019-Monastir, Tunisia

Received: 01 February 2020 Revised: 01 February 2020
Primary: 28A20; Secondary: 28A80

The aim of this article is to show that the multifractal Hausdorff and packing measures are mutually singular, which in particular provides an answer to Olsen's questions.
- Multifractal analysis,
- homogeneous Moran sets
Citation: Zied Douzi, Bilel Selmi. On the mutual singularity of multifractal measures[J]. Electronic Research Archive, 2020, 28(1): 423-432. doi: 10.3934/era.2020024

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Abstract

The aim of this article is to show that the multifractal Hausdorff and packing measures are mutually singular, which in particular provides an answer to Olsen's questions.

References

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