论文标题
一项关于完整度量空间中量化维度的研究
A study on Quantization Dimension in complete metric spaces
论文作者
论文摘要
本文的主要目的是开发与迭代功能系统相关的不变度度量的量化理论，该功能系统由一个完整的度量空间中有限数量的承包无限相似。这将欧几里得空间中自相似度量的量化维度的量化范围概括为完整的度量空间。在最后一部分中，讨论了量化维度的连续性。
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.
