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Locally uniform approximation by solutions of the classical Dirichlet problem. (English) Zbl 0773.31010
Let $$U$$ be an open subset of a $${\mathcal P}$$-harmonic space. It is shown that, in the topology of local uniform convergence, the space of classical solutions of the Dirichlet problem on $$U$$ is dense in the space of Perron-Wiener-Brelot solutions of the Dirichlet problem if and only if the irregular boundary points of $$U$$ form a set of harmonic measure 0.

##### MSC:
 31D05 Axiomatic potential theory 35A35 Theoretical approximation in context of PDEs
##### Keywords:
harmonic space; irregular boundary points
Full Text:
##### References:
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