In complex analysis, Harnack's principle is a theorem about the behavior of sequences of harmonic functions.

If the functions u₁(z), u₂(z), ... are harmonic in an open subset G of the complex plane C, and

in every point of G, then the limit

either is infinite in every point of the domain G or it is finite in every point of the domain, in both cases uniformly in each closed subset of G. In the latter case, the function

is harmonic in the set G.