### Abstract

Let e{open} be the family of all continua E in {Mathematical expression}, where U={|z| < 1}, let U(E) be the connected component of UE containing the point z=0, let w_{E}(z_{0}=w(z_{0}, E, U(E)) be the harmonic measure of E relative to the domain U(E) at the point z_{0} ∃ U(E). In the paper one answers affirmatively a question raised by B. Rodkin [K. F. Barth, D. A. Branna, and W. K. Hayman, "Research problems in complx analysis," Bull. London Math. Soc., l6, No. 5, 490-517, 1984]. Namely, one proves that in the family e{open}(d_{0}) of continua E ∃ e{open}, satisfying the condition diam E=d_{0},o<d_{0}≤2, one has the inequality {Mathematical expression} arcsin d_{0}/2, one indicates all the cases for which equality prevails.

Original language | English |
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Pages (from-to) | 2140-2142 |

Number of pages | 3 |

Journal | Journal of Soviet Mathematics |

Volume | 38 |

Issue number | 4 |

DOIs | |

State | Published - Aug 1987 |