关于有界度图的$p$ -Royden和$p$ -调和边界的一些结果
Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree
摘要：
设$p$是大于1的实数，$Γ$是有界度的连通图.证明了去掉$p$ -调和边界后的$Γ$的$p$ -Royden边界是一个$F_σ$ -集.我们还刻画了$Γ$中单侧无限路的某个子集的极值点的交点作为$Γ$的$p$ -调和边界.
英文摘要：
Let $p$ be a real number greater than one and let $Γ$ be a connected graph of bounded degree. We show that the $p$-Royden boundary of $Γ$ with the $p$-harmonic boundary removed is a $F_σ$-set. We also characterize the $p$-harmonic boundary of $Γ$ in terms of the intersection of the extreme points of a certain subset of one-sided infinite paths in $Γ$.
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