Some results concerning the p-Royden and p-harmonic boundaries of a graph of bounded degree
Michael J. Puls · Annales Academiae Scientiarum Fennicae Mathematica · 2012
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.