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INTERMEDIATE ASSOUAD-LIKE DIMENSIONS FOR MEASURES
Fractals ( IF 4.7 ) Pub Date : 2020-08-22 , DOI: 10.1142/s0218348x20501431
KATHRYN E. HARE 1 , KEVIN G. HARE 1
Affiliation  

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, [Formula: see text]-Assouad spectrum, and [Formula: see text]-dimensions. In this paper, we study the analogue of the upper and lower [Formula: see text]-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.

中文翻译:

测量的中间尺寸

度量空间的上下 Assouad 维度是空间盒子维度的局部变体,并提供关于集合中“最厚”和“最薄”部分的定量信息。已经介绍了这些集合维度的不太极端的版本,包括上和下准 Assouad 维度、[公式:参见文本]-Assouad 谱和 [公式:参见文本]-维度。在本文中,我们研究了上、下[公式:见正文]的类比——度量的维度。我们给出了这些维度的一般属性,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结果。
更新日期:2020-08-22
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