Harnack's second convergence theorem

Harnack's second convergence theorem

[′här·naks ¦sek·ənd kən′vər·jəns ‚thir·əm]
(mathematics)
The theorem that if a sequence of functions is harmonic in a common domain of three-dimensional space and their values are monotonically decreasing at any point in the domain, then convergence of the sequence at any point in the domain implies uniform convergence of the sequence in every closed subregion of the domain to a function which is itself harmonic.