论文标题
LIMSUP集合在公制空间中的大型交点属性
Large intersection property for limsup sets in metric space
论文作者
论文摘要
我们表明，limsup集由紧凑型ahlfors $ s $ s $ regular space $（x，x，\ mathscr {b}，μ，ρ）$产生的limsup集属于与index $λ$的大相交的类别，由$ \ m nathcal {g}^g}^λ（x x x）$ sodex $λ$属于$ undex $λ$。特别是，这提供了此类集合的Hausdorff维度的下限。这些结果适用于获得带有指数$γ_2$和$δ$的LIMSUP随机分形，属于$ \ Mathcal {g}^{s-δ-γ_2}（x）$，几乎可以肯定，随机覆盖集，带有指数式混合属性属于$ \ Mathcal属于$ \ nter $ \ nter $ see $ suery $ suely $ suely $ sure suriely surecy surecy sure surecy surecy surecy n wer wery s_ s_0} s_0} s_0} s_0}（x）覆盖集的Hausdorff尺寸几乎肯定。我们还研究了矩形在度量空间中产生的LIMSUP集的大交点。
We show that limsup sets generated by a sequence of open sets in compact Ahlfors $s$-regular space $(X,\mathscr{B},μ,ρ)$ belong to the classes of sets with large intersections with index $λ$, denoted by $\mathcal{G}^λ(X)$, under some conditions. In particular, this provides a lower bound on Hausdorff dimension of such sets. These results are applied to obtain that limsup random fractals with indices $γ_2$ and $δ$ belong to $\mathcal{G}^{s-δ-γ_2}(X)$ almost surely, and random covering sets with exponentially mixing property belong to $\mathcal{G}^{s_0}(X)$ almost surely, where $s_0$ equals to the corresponding Hausdorff dimension of covering sets almost surely. We also investigate the large intersection property of limsup sets generated by rectangles in metric space.
