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Frostman and Fourier characterisations of fractal dimensions

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.

preprint2026arXivOpen access
Kenneth J. FalconerShuqin Zhang
math.MG
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Open access2 authors1 topic
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Kenneth J. FalconerShuqin Zhang

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