关于测度的上正则维数
On the upper regularity dimensions of measures
摘要：
我们研究了\emph{upper regularity dimension}，它描述了测度的极端局部标度行为，并有效地量化了\emph{doubling}的概念。我们对上正则维数进行了深入的研究，包括它与Assouad维数、上局部维数、$L^q$ -谱和弱切测度等概念的关系.我们还计算上的正则维数明确在一些重要的情况下，包括自相似措施，自仿射措施，和措施的序列。
英文摘要：
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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