Definitions and preliminary discussions

  • Kiyoshi Noshiro
Part of the Ergebnisse der Mathematik und Ihrer Grenzgebiete book series (MATHE2, volume 28)


Let D be an arbitrary domain1 with boundary Γ. Let E be a totally disconnected closed set contained in Γ. We suppose that w = f(z) is non-constant, single-valued and meromorphic in D. We associate with every point z0 of Γ the following: sets of values.


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  1. 1.
    Nevanlinna [6], p. 291.Google Scholar
  2. 2.
    Concerning notions of analytic continuation of algebraic character and (ordinary or essential) transcendental singularity, cf. Collingwood and Cartwright [1], pp. 99–103; Noshiro [4], pp. 43–73.Google Scholar
  3. 3.
    Iversen’s property of analytic functions has been systematically investigated by Stoïlow [1, 9].Google Scholar
  4. 1.
    Nevanlinna [6], p. 292.Google Scholar
  5. 2.
    This means that a is taken by w = f(z) only finite times in |z| < ∞.Google Scholar

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© Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1960

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  • Kiyoshi Noshiro

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