完全度量空间中量子化维数的研究
A study on Quantization Dimension in complete metric spaces
摘要：
本文的主要目的是在完全度量空间中建立由有限个压缩无穷小相似项组成的迭代函数系统的不变测度的量子化维数理论。这将欧几里得空间中自相似测度的量子化维数的已知结果推广到完全度量空间。最后讨论了量子化维数的连续性。
英文摘要：
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a complete metric space. This generalizes the known results on quantization dimension of self-similar measures in the Euclidean space to a complete metric space. In the last part, continuity of quantization dimension is discussed.
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