The Outer Regularity of the Hewitt-Stromberg Measures in a Metric Space and Applications

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Authors

  • Zied Douzi
     Analysis, Probability and Fractals Laboratory LR18ES17 Department of Mathematics, Faculty of Sciences, University of Monastir, 5000-Monastir ,TN
  • Bilel Selmi
     Analysis, Probability and Fractals Laboratory LR18ES17 Department of Mathematics, Faculty of Sciences, University of Monastir, 5000-Monastir ,TN

DOI:

https://doi.org/10.18311/jims/2024/31831

Keywords:

Multifractal Formalism, Hewitt-Stromberg Measures, Doubling Measures, Inhomogeneous Moran Measures.

Abstract

The aim of this paper is to show that if the Hewitt-Stromberg pre-measures are finite, then these pre-measures have a kind of outer regularity in a general metric space X. We also give some conditions on the Hewitt-Stromberg pre-measures such that the Hewitt-Stromberg measures are regular on a complete separable metric space X. In addition, if the measure µ satisfies the doubling condition then the Hewitt-Stromberg pre-measure and measure are both zero or nonzero. As an application, we obtain new sufficient conditions for the valid refined multifractal formalism which is based on the Hewitt-Stromberg measures.

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Published

2024-07-01

How to Cite

Douzi, Z., & Selmi, B. (2024). The Outer Regularity of the Hewitt-Stromberg Measures in a Metric Space and Applications. The Journal of the Indian Mathematical Society, 91(3-4), 303–320. https://doi.org/10.18311/jims/2024/31831

Issue

Volume 91, Issue 3-4, July-December 2024

Section

Articles

License

Copyright (c) 2024 Bilel Selmi, Zied Douzi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-10-30
Accepted 2023-06-19
Published 2024-07-01

 

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