Harnack's theorem

In complex analysis, Harnack's principle or Harnack's theorem is one of several closely related theorems about the convergence of sequences of harmonic functions, that follow from Harnack's inequality.

If the functions ${\displaystyle u_{1}(z)}$, ${\displaystyle u_{2}(z)}$, ... are harmonic in an open connected subset ${\displaystyle G}$ of the complex plane C, and

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