Frostman and Fourier characterisations of fractal dimensions

Published 27 May 2025 in math.MG | (2505.21217v1)

Abstract: 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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