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arXiv · 1706.09340

On the upper regularity dimensions of measures

Jonathan M. Fraser·Douglas C. Howroyd
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Abstract

We study the \emph{upper regularity dimension} which describes the extremal local scaling behaviour of a measure and effectively quantifies the notion of \emph{doubling}. We conduct a thorough study of the upper regularity dimension, including its relationship with other concepts such as the Assouad dimension, the upper local dimension, the $L^q$-spectrum and weak tangent measures. We also compute the upper regularity dimension explicitly in a number of important contexts including self-similar measures, self-affine measures, and measures on sequences.

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Jonathan M. Fraser, Douglas C. Howroyd. 2017-06-28. On the upper regularity dimensions of measures. https://arxiv.org/abs/1706.09340

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