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1. On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide

Author

Bilel Selmi and Zied Douzi

Subjects
Pure mathematics, Applied Mathematics, General Mathematics, Numerical analysis, 010102 general mathematics, Dimension (graph theory), Multifractal system, 01 natural sciences, 010305 fluids & plasmas, Singularity, Fractal, Homogeneous, 0103 physical sciences, 0101 mathematics, Algebra over a field, GEOM, Mathematics
Abstract

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.

Published
2021

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