About the Jones-Wolff Theorem on the Hausdorff dimension of harmonic measure

Abstract

These are the lecture notes of a seminar held at the Universitat Aut\`onoma de Barcelona where the Jones-Wolff theorem about the dimension of harmonic measure in the plane is explained in full detail, for non-expert readers.Comment: The definition of Green's function used in the proof of Lemma 1 in the previous version of the preprint was only valid for bounded domains. This is corrected in this new versio