Pajot, Hervé Covering theorem by Ahlfors-regular sets and analytic capacity. (Théorème de recouvrement par des ensembles Ahlfors-réguliers et capacité analytique.) (French) Zbl 0863.30033 C. R. Acad. Sci., Paris, Sér. I 323, No. 2, 133-135 (1996). 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). Reviewer: J.Burbea (Pittsburgh) Cited in 3 Documents 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 Keywords:analytic capacity; removable set; rectifiable set; regular set; Hausdorff measure PDF BibTeX XML Cite \textit{H. Pajot}, C. R. Acad. Sci., Paris, Sér. I 323, No. 2, 133--135 (1996; Zbl 0863.30033)