The multifractal box dimensions of typical measures
Fr\'ed\'eric Bayart
TL;DR
This paper investigates the typical multifractal box dimensions of measures on compact subsets of Euclidean space, providing new insights even in the context of box dimensions of measures.
Contribution
It introduces the computation of typical multifractal box dimensions of measures, a novel result in the study of measure dimensions.
Findings
Established the typical multifractal box dimensions for measures on compact sets.
Provided new theoretical results in the context of box dimensions of measures.
Extended understanding of measure dimensions in Euclidean spaces.
Abstract
We compute the typical (in the sense of Baire's category theorem) multifractal box dimensions of measures on a compact subset of . Our results are new even in the context of box dimensions of measures.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory