Rectifiability of Harmonic Measure


In the present paper we prove that for any open connected set Ω ⊂ R, n ≥ 1, and any E ⊂ ∂Ω with 0 < H(E) < ∞ absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E implies that ω|E is rectifiable. CONTENTS 


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