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Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$ ,
We present a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz [RR].More precisely, we establish scale invariant absolute continuity of harmonic measure with respect to surface measure, along with higher integrability of the Poisson kernel, for a domain Ω ⊂ R n+1 , n ≥ …