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THE MEASURABILITY OF HEWITT-STROMBERG MEASURES AND DIMENSIONS

  • Zied Douzi (Analysis, Probability and Fractals Laboratory: LR18ES17 Faculty of Sciences of Monastir Department of Mathematics) ;
  • Bilel Selmi (Analysis, Probability and Fractals Laboratory: LR18ES17 Faculty of Sciences of Monastir Department of Mathematics) ;
  • Haythem Zyoudi (Analysis, Probability and Fractals Laboratory: LR18ES17 Faculty of Sciences of Monastir Department of Mathematics)
  • Received : 2022.05.28
  • Accepted : 2022.09.16
  • Published : 2023.04.30
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Abstract

The aim of this paper is to study the descriptive set-theoretic complexity of the Hewitt-Stromberg measure and dimension maps.

Keywords

Acknowledgement

The second author would like to thank Professors Lars Olsen and Jinjun Li for useful discussions while writing this manuscript and for pointing out that the upper (fractal/multifractal) Hewitt-Stromberg function can be is not necessarily a metric outer measure. He is also greatly indebted to Professor Pertti Mattila for giving elaborate comments so that the presentation can be greatly improved. This work was supported by Analysis, Probability & Fractals Laboratory (No: LR18ES17).

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