In the context of an infinite network $N$, the Dirichlet problem with respect to an arbitrary subset of vertices $N$ is solved.Using this solution, some of the important potential-theoretic concepts like Balayage, Domination principle, and Poisson kernel are investigated in $N$.
"Potential-theoretic study of functions on an infinite network." Hokkaido Math. J. 37 (1) 59 - 73, February 2008. https://doi.org/10.14492/hokmj/1253539587