Prove that if a sequence of harmonic function on the open disk converges uniformlyon compact subset of the disk,then the limit is harmonic.

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I let {${u_n}$}is a sequence of harmonic functions defined on an open disk and $|u_n|≤M$,where {$u_n$}satisfying $u_n(x)$$u(x)$ for a.e.$x$ as n tends to infinity.

And then I can't think of any way in complex analysis that I can keep doing this problem, so I'm going to use the formula I learned in real analysis, right

$$\int u(x)dx=lim_{n→∞}\int u_n( x)dx$$

But then I don't know how to use the harmonic function and the compact set and who can give me a little help, thank you very much