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Proceedings of the American Mathematical Society

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Positive length but zero analytic capacity


Author: John Garnett
Journal: Proc. Amer. Math. Soc. 26 (1970), 696-699
MSC: Primary 30.41
DOI: https://doi.org/10.1090/S0002-9939-1970-0276456-5
MathSciNet review: 0276456
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  • [1] Arnaud Denjoy, Sur la continuité des fonctions analytiques singulières, Bull. Soc. Math. France 60 (1932), 27–105 (French). MR 1504984
  • [2] L. D. Ivanov, On Denjoy’s conjecture, Uspehi Mat. Nauk 18 (1963), no. 4 (112), 147–149 (Russian). MR 0156995
  • [3] A. G. Vituškin, Example of a set of positive length but of zero analytic capacity, Dokl. Akad. Nauk SSSR 127 (1959), 246–249 (Russian). MR 0118838
  • [4] Lawrence Zalcmann, Analytic capacity and rational approximation, Lecture Notes in Mathematics, No. 50, Springer-Verlag, Berlin-New York, 1968. MR 0227434

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DOI: https://doi.org/10.1090/S0002-9939-1970-0276456-5
Article copyright: © Copyright 1970 American Mathematical Society