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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