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On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide
Ricerche di Matematica ( IF 1.1 ) Pub Date : 2021-04-02 , DOI: 10.1007/s11587-021-00572-6 Zied Douzi , Bilel Selmi
中文翻译:
关于休伊特–斯特伦伯格测度的奇异性,其中多重分形函数不一定重合
更新日期:2021-04-02
Ricerche di Matematica ( IF 1.1 ) Pub Date : 2021-04-02 , DOI: 10.1007/s11587-021-00572-6 Zied Douzi , Bilel Selmi
In this paper, we attain the multifractal Hewitt–Stromberg dimension functions of Moran measures associated with homogeneous Moran fractals and show that the multifractal Hewitt–Stromberg measures are mutually singular for which the multifractal functions do not necessarily coincide. In particular, we give a positive answer to questions posed in Attia and Selmi (J Geom Anal 31:825-862, 2021) and discuss some interesting examples.
中文翻译:
关于休伊特–斯特伦伯格测度的奇异性,其中多重分形函数不一定重合
在本文中,我们获得了与均质Moran分形相关的Moran测度的多重分形Hewitt–Stromberg维数函数,并证明了多重分形的Hewitt–Stromberg测度是相互奇异的,因此多重分形函数不一定重合。特别是,我们对Attia和Selmi(J Geom Anal 31:825-862,2021)中提出的问题给出了肯定的答案,并讨论了一些有趣的示例。