Subharmonic functions in n-connected domains

Abstract

In this paper we investigate some of the properties of harmonic and subharmonic functions defined on n-connected domain G. In particular, we study the behavior of subharmonic functions at every point of the boundary of G. We prove that if f is subharmonic and u f is the least harmonic majorant of f then the lim sup taken along the normal to the boundary of G of f(z) P(z, x) converges to the singular part of the boundary measure of u f evaluated at x. The result is true for every x belonging to the boundary of G.