The α-dimensional measure of the graph and set of zeros of a Brownian path
The α-dimensional measure of the graph and set of zeros of a Brownian path
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图的 α 维测度和布朗路径的零点集
DOI：
10.1017/s030500410003019x
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发表时间：
1955
影响因子：
0.8
通讯作者：
S. Taylor
中科院分区：
文献类型：
--
作者：
S. Taylor
在最近与Besicovitch教授的联合论文（1）中，我们宣布了这样的猜想：对于几乎所有的一维布朗路径，零点集的维数为1/2，A 1/2-测度为零。本文的目的是证明这个结果。在这样做时，我们考虑布朗路径ω的图C（ω）作为平面上的点集，并证明，以概率1，C（ω）具有维数H2和零Λ H2-测度。
In a recent joint paper (1) with Prof. Besicovitch we announced the conjecture that for almost all one-dimensional Brownian paths, the set of zeros has dimensional number ½, and zero A½-measure. It is the purpose of this paper to give a proof of this result. In doing so we consider the graph C(ω) of a Brownian path ω as a point set in the plane, and prove that, with probability 1, C(ω) has dimensional number ¾ and zero Λ¾-measure.