Some results concerning the p-Royden and p-harmonic boundaries of a graph of bounded degree

Abstract

Abstract. 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 an 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.

The -Harmonic Boundary and -Massive Subsets of a Graph of Bounded Degree

“…For each n ∈ N, set P 1/n = {γ ∈ P F \ P ∞ | |h(γ) − c h | > 1/n}. Now suppose that λ p (P 1/n ) < ∞ for some n ∈ N. By [12,Lemma 5.2], γ {Ex(γ) | γ ∈ P 1/n } ∩ ∂ p (Γ) ∅.…”