论文标题
设定有限状态的原理的点
A point to set principle for finite-state dimension
论文作者
论文摘要
有效维度已通过点对集合原理\ cite {lulu18} \在几何度量理论中非常有用，该原理通过相关的有效维度来表征Hausdorff维度。在此上下文中，有限状态维度是最高要求的有效性\ cite {fsd} \，除其他结果外，可以用来表征Borel正态性\ cite {bohivi05}。 在本文中，我们证明了有限状态维度的特征，以一定精度的真实数字的信息内容来表征。然后，我们使用这种特征来提供相对态度的强大概念，并证明有限状态的维度点对上原理。我们最后一个关于相对正态性的等分分配属性的公开问题。
Effective dimension has proven very useful in geometric measure theory through the point-to-set principle \cite{LuLu18}\ that characterizes Hausdorff dimension by relativized effective dimension. Finite-state dimension is the least demanding effectivization in this context \cite{FSD}\ that among other results can be used to characterize Borel normality \cite{BoHiVi05}. In this paper we prove a characterization of finite-state dimension in terms of information content of a real number at a certain precision. We then use this characterization to give a robust concept of relativized normality and prove a finite-state dimension point-to-set principle. We finish with an open question on the equidistribution properties of relativized normality.
