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It is a well-known folklore result that quantitative, scale invariant absolute continuity (more precisely, the weak-A∞ property) of harmonic measure with respect to surface measure, on the bound¬ary of an open set Ω ⊂ ℝn+1 with Ahlfors-David regular boundary, is equivalent to the solvability of the Dirichlet problem in Ω, with data in Lp(∂ Ω) for some p < ∞. Drawing an analogy to the famous Wiener...
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