论文标题
措施的点端尺寸
Pointwise Assouad dimension for measures
论文作者
论文摘要
我们引入了Assouad维度的指标措施的一个点式变体，并研究其与全球Assouad维度相关的特性。我们表明，通常，Assouad维度的值与全局对应物的值不同，但是在许多经典情况下，它表现出与经典局部维度相似的精确维度属性，即几乎在每个点等于全局Assouad维度。我们还通过支持强烈分开的自符号组集的位置依赖概率来计算不变措施的Assouad维度。
We introduce a pointwise variant of the Assouad dimension for measures on metric spaces, and study its properties in relation to the global Assouad dimension. We show that, in general, the value of the pointwise Assouad dimension differs from the global counterpart, but in many classical cases, it exhibits similar exact dimensionality properties as the classical local dimension, namely it equals the global Assouad dimension at almost every point. We also compute the Assouad dimension of invariant measures with place dependent probabilities supported on strongly separated self-conformal sets.
