论文标题
具有指数混合属性的度量空间中的随机覆盖集
Random Covering Sets in Metric Space with Exponentially Mixing Property
论文作者
论文摘要
Let $\{B(ξ_n,r_n)\}_{n\ge1}$ be a sequence of random balls whose centers $\{ξ_n\}_{n\ge1}$ is a stationary process, and $\{r_n\}_{n\ge1}$ is a sequence of positive numbers decreasing to 0. Our object is the random覆盖集合$ e = \ limsup \ limits_ {n \ to \ infty} b（ξ_n，r_n）$，即$ b（ξ_n，r_n）$ cover的点。 $ e $的尺寸从度量，维度和拓扑的角度进行了研究。
Let $\{B(ξ_n,r_n)\}_{n\ge1}$ be a sequence of random balls whose centers $\{ξ_n\}_{n\ge1}$ is a stationary process, and $\{r_n\}_{n\ge1}$ is a sequence of positive numbers decreasing to 0. Our object is the random covering set $E=\limsup\limits_{n\to\infty}B(ξ_n,r_n)$, that is, the points covered by $B(ξ_n,r_n)$ infinitely often. The sizes of $E$ are investigated from the viewpoint of measure, dimension and topology.
