关于调和测度的三重点的Tsirelson定理
On Tsirelson's theorem about triple points for harmonic measure
摘要：
Tsirelson在1997年的一个定理中指出，给定$\mathbb R^{n+1}$中的三个不相交区域，属于三个边界的交点的三重点的集合，其中三个相应的调和测度是相互绝对连续的，有零调和测度。Tsirelson的原始证明是基于对布朗运动和Walsh-布朗运动的滤子的精细分析，不能转化为位势论的论证。在本文中，我们给出了一个纯粹的分析证明相同的结果。
英文摘要：
A theorem of Tsirelson from 1997 asserts that given three disjoint domains in $\mathbb R^{n+1}$, the set of triple points belonging to the intersection of the three boundaries where the three corresponding harmonic measures are mutually absolutely continuous has null harmonic measure. The original proof by Tsirelson is based on the fine analysis of filtrations for Brownian and Walsh-Brownian motions and can not be translated into potential theory arguments. In the present paper we give a purely analytical proof of the same result.
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