时间：2024年10月16日（周三）14:00-15:00

Time: 14:00-15:00, Wednesday, October 16 2024

地点：西湖大学云谷校区E4-233

Venue: E4-233, Yungu Campus

主持人/Host：Thierry De Pauw, ITS

主讲人/Speaker：Hui Rao, Central China Normal University

主讲人简介/Biography：Professor Hui Rao obtained his bachelor degree from Sichuan University and his master and doctoral degrees from Wuhan University. He held positions at many institutions including Wuhan University, Tsinghua University, Nanjing University, The Chinese University of Hong-Kong, and Tsuda College. He is now a Professor at Central China Normal University. His work is on fractal geometry, tiling theory, and symbolic dynamic system.

讲座主题/Title：Box-counting measures of metric spaces

讲座摘要/Abstrct: In a metric space (X, d), a measure μ is called an Ahlfors regular measure if the measure of any ball with radius r is proportional to r^s for some constant s. Ahlfors regular measure plays an important role in analysis of metric spaces. We introduce a notion of box-counting measure, where μ(A) measures the number of δ-boxes intersecting a set A. Indeed, this measure is a generalization of Ahlfors regular measure. For general self-affine sets, there exist box-counting measures but there does not exist Ahlfors measure. First, we show that the multi-fractal spectrum of a box-counting measure is a Lipschitz invariant. Secondly, we show that any bi Lipschitz map between two metric spaces with box-counting measures are (locally) measure preserving.