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Covering theorem by Ahlfors-regular sets and analytic capacity. (Théorème de recouvrement par des ensembles Ahlfors-réguliers et capacité analytique.) (French) Zbl 0863.30033
Under a density condition, the author, using the Mattila, Melnikov and Verdera theorem [Ann. Math. (to appear)], proves that every compact, purely non 1-rectifiable planar set of finite 1-dimensional Hausdorff measure has a zero analytic capacity (i.e. is removable for bounded holomorphic functions).

##### MSC:
 30C85 Capacity and harmonic measure in the complex plane 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane 28A78 Hausdorff and packing measures