Ahlfors version of this theorem says that a sequence of harmonic functions {Un} tends UNIFORMLY to infinity on compact subsets, or tends to a harmonic limit function uniformly on compact sets.(adsbygoogle = window.adsbygoogle || []).push({});

Can someone please clarify what tending uniformly to infinity means?

In particular, it seems like a set of harmonic {Un} where Uk = k (such that each function is constant) tends non-uniformly to infinity.

So I must be missing something somewhere.

thanks

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# Harnack's Principle question

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