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Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges

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Abstract

The aim of this paper is to show that if the Hewitt–Stromberg pre-measures with respect to the gauge are finite, then these pre-measures have a kind of outer regularity in a general metric space X. We give also some conditions on the Hewitt–Stromberg pre-measures with respect to the gauge such that the Hewitt–Stromberg measures have an almost inner regularity on a complete separable metric space X.

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Acknowledgements

We would like to thank the anonymous referees for valuable comments and suggestions that led to the improvement of the manuscript. We especially appreciate the referee’s attentive reading of the second submitted version of this manuscript and his/her corrections to the proof of Theorem 3.

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Authors and Affiliations

  1. Analysis, Probability and Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000, Monastir, Tunisia

    Z. Douzi & B. Selmi

  2. School of Science, East China University of Technology, Nanchang, Jiangxi, 330013, People’s Republic of China

    Z. Yuan

Authors
  1. Z. Douzi
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  2. B. Selmi
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  3. Z. Yuan
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Corresponding author

Correspondence to Z. Douzi.

Additional information

This work was supported by Analysis, Probability & Fractals Laboratory (No: LR18ES17).

Z. Yuan is supported by the National Natural Science Foundation of China (Grant No. 12061006) and Natural Science Foundation of Jiangxi (Grant No. 20212BAB201002).

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Douzi, Z., Selmi, B. & Yuan, Z. Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges. Anal Math 49, 733–746 (2023). https://doi.org/10.1007/s10476-023-0227-1

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  • DOI: https://doi.org/10.1007/s10476-023-0227-1

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