ASSOUAD DIMENSION: ANTIFRACTAL METRIZATION, POROUS SETS, AND HOMOGENEOUS MEASURES
ASSOUAD DIMENSION: ANTIFRACTAL METRIZATION, POROUS SETS, AND HOMOGENEOUS MEASURES
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发表时间：
1998
影响因子：
0.6
通讯作者：
J. Luukkainen
中科院分区：
文献类型：
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作者：
J. Luukkainen
证明了非空可分度量空间X存在一个完全有界度量，使得X的度量维数在Assouad意义下等于X的拓扑维数，从而得到了拓扑维数的一个刻画.我们也给出了一个特征的基础上Assouad维数的维数（嵌入维数）的紧集在欧氏空间。我们讨论了Assouad维数和这些结果与多孔集和措施的双重性质。在附录中证明了Assouad维数的基本性质。
We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.