This article explores fractal properties of dominated self-affine measures, suggesting broader applicability of local dimension spectrum.
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By analyzing exact dimensionality, we obtain deterministic results that extend the scope of the local dimension spectrum beyond the almost-sure setting.
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Batsis et al. (2026) studied this question.
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