Abstract
The aim of this work is to provide a representation of the multifractal Hausdorff and packing dimensions of compact sets in the Euclidean space in terms of the lower and upper local $$(q,\mu )$$ -dimensions of a probability measure on $$\mathbb {R}^n$$ , respectively. In addition, a relationship is established allowing to determine the Olsen’s multifractal functions by means of the corresponding measures’ versions. The multifractal functions are defined as the supremum over the lower and upper multifractal dimensions of all Borel probability measures.
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