测度的逐点加倍指数及其在Bedford-McMullen地毯双Lipschitz分类中的应用
Point-wise doubling indices of measures and its application to bi-Lipschitz classification of Bedford-McMullen carpets
AI总结：
本文引入逐点加倍指数以刻画非加倍测度，计算了Bedford-McMullen地毯上均匀Bernoulli测度的该指数，并据此证明除一小类外，双Lipschitz等价的地毯具有相同纤维序列（至多相差一个置换）。
摘要：
加倍测度由Beurling和Ahlfors于1956年引入，现已成为度量空间分析中的一个基本概念。本文针对非加倍测度，引入了逐点加倍指数的概念，并计算了Bedford-McMullen地毯上均匀Bernoulli测度的逐点加倍指数。作为应用，我们证明，除一小类Bedford-McMullen地毯外，若两个Bedford-McMullen地毯双Lipschitz等价，则它们具有相同的纤维序列（至多相差一个置换）。
英文摘要：
Doubling measure was introduced by Beurling and Ahlfors in 1956 and now it becomes a basic concept in analysis on metric space. In this paper, for a measure which is not doubling, we introduce a notion of point-wise doubling index, and calculate the point-wise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets. As an application, we show that, except a small class of Bedford-McMullen carpets, if two Bedford-McMullen carpets are bi-Lipschitz equivalent, then they have the same fiber sequence up to a permutation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
