If the functions $u_1(z)$ $u_2(z)$ ... are harmonic in the domain $G \subseteq\mathbb{C}$ , and $$u_1(z) \le u_2(z) \le \cdots$$ in every point of $G$ then $\lim_{n\to\infty}u_n(z)$ , either is infinite in every point of the domain or it is finite in every point of the domain, in both cases uniformly in each closed subdomain of $G$ In the latter case, the function $u(z) = \lim_{n\to\infty}u_n(z)$ , is harmonic in the domain $G$ (cf. limit function of sequence).