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Reports properties of fractal dimensions using Frostman criteria in mathematical sets, suggesting new insights.
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension. We also express a number of fractal dimensions in terms of Fourier properties of measures.
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Falconer et al. (2026) studied this question.
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