On the dimension of p-harmonic measure

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Boundary Harnack Principle for p-harmonic Functions in Smooth Euclidean Domains (2007, background): “While in R(2) the results in [10] are far more general than ours, it seems that their method does not extend to higher dimensions; see Lemma 2.”
Regularity and Free Boundary Regularity for the p-Laplace Operator in Reifenberg Flat and Ahlfors Regular Domains (2012, unknown): “We note that (iii) in our definition of NTA-domains below is different but equivalent to the usual Harnack chain condition given in [16] (see [4], Lemma 2.”