摘要：Given any Bernoulli measure μ that is ×3 invariant (such as the Cantor-Lebesgue measure on the ternary Cantor set) and an irrational number t, it holds that for almost all x with respect to μ, the product tx is 3 normal—meaning that the orbit of tx under the ×3 map is uniformly distributed on [0, 1]. This nice result was recently proved by Dayan, Ganguly, and Barak Weiss using sophisticated techniques from random walk theory. We will present a new proof of the Dayan-Ganguly-Weiss result, utilizing recent advancements in the study of self-similar measures with overlaps. Our approach extends the result to cases where the measure μ is only required to be invariant, ergodic, and of positive dimension.

个人简介：湖南大学数学学院教授、博士生导师，2013 年 6 月获法国皮卡第大学博士学位。主要从事分形几何、几何测度论、动力系统与遍历理论等方向研究，先后在芬兰奥卢大学、以色列爱因斯坦数学研究所等机构做博士后研究，在 Annals of Math.、Adv.Math. 等国际一流数学期刊发表多篇论文。解决了 H. Furstenberg 1969 年提出的交集猜想，获 2023 年 ICCM 鲍剑文最佳论文奖、2025 年国际基础科学大会 “前沿科学奖”。