Definition
Let D be a bounded, open domain in n-dimensional Euclidean space Rn, n ≥ 2, and let ∂D denote the boundary of D. Any continuous function f : ∂D → R determines a unique harmonic function Hf that solves the Dirichlet problem
If a point x ∈ D is fixed, by the Riesz representation theorem and the maximum principle Hf(x) determines a probability measure ω(x, D) on ∂D by
The measure ω(x, D) is called the harmonic measure (of the domain D with pole at x).
Read more about this topic: Harmonic Measure
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