论文标题
中间的指标尺寸
Intermediate Assouad-like dimensions for measures
论文作者
论文摘要
公制空间的上部和下部Assouad尺寸是该空间框尺寸的局部变体，并提供了有关该集合的“最厚”和“最薄”部分的定量信息。已经引入了这些尺寸的极端版本，包括上和下级式尺寸，$θ$ -assouad Spectrum和$φ$ -Dimensions。在本文中，我们研究了措施的上和下$ $ $限制的类似物。我们提供了此类维度的一般特性，以及满足各种分离属性和离散度量的自相似度量的更具体的结果。
The upper and lower Assouad dimensions of a metric space are local variants of the box dimensions of the space and provide quantitative information about the `thickest' and `thinnest' parts of the set. Less extreme versions of these dimensions for sets have been introduced, including the upper and lower quasi-Assouad dimensions, $θ$-Assouad spectrum, and $Φ$-dimensions. In this paper, we study the analogue of the upper and lower $Φ$-dimensions for measures. We give general properties of such dimensions, as well as more specific results for self-similar measures satisfying various separation properties and discrete measures.
