Local dimensions in Moran constructions
Antti K\"aenm\"aki, Bing Li, Ville Suomala
TL;DR
This paper investigates the local and $L^q$-dimensions of Moran sets and measures within doubling metric spaces, extending previous results to deepen understanding of their fractal properties.
Contribution
It generalizes and extends existing results on the dimensional properties of Moran sets and measures in doubling metric spaces.
Findings
Analysis of local dimensions in Moran constructions
Extension of $L^q$-dimension results
Broader applicability in doubling metric spaces
Abstract
We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and -dimensions. We generalize and extend several existing results in this area.
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