Harnack’s principle
If the functions , , … are harmonic (http://planetmath.org/HarmonicFunction) in the domain and
in every point of , then either is infinite in every point of the domain or it is finite in every point of the domain, in both cases uniformly (http://planetmath.org/UniformConvergence) in each closed (http://planetmath.org/ClosedSet) subdomain of . In the latter case, the function is harmonic in the domain (cf. limit function of sequence).