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On Exceptional Values of a Meromorphic Function

Published online by Cambridge University Press:  22 January 2016

Makoto Ohtsuka
Makoto Ohtsuka*
Affiliation:
Mathematical Institute, Nagoya University
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M. Brelot [1] has shown that if u(z) is subharmonic in an open set D in the z-plane with boundary C and is bounded from above in a neighborhood of a boundary point z0, which is contained in a set E ⊂ C of inner harmonic measure zero with respect to D, and such that z0 is a regular point for Dirichlet problem in D, then

(1) .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 9 , October 1955 , pp. 119 - 121
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

[1] Brelot, M.: Sur l’allure à la frontière des fonctions harmoniques, sousharmoniques ou holomorphes, Bull. Soc. Roy. Liège. (1939). pp. 468–477.Google Scholar
[2] Brelot, M.: Le problème de Dirichlet ramifié, Ann. Univ. Grenoble, 22 (1946), pp. 167–200.Google Scholar
[3] Kametani, S.: The exceptional values of functions with the set of capacity zero of essential singularities, Proc. Imp. Acad. Tokyo, 17 (1941), pp. 429–433.Google Scholar
[4] Noshiro, K.: On the singularities of analytic functions. -Jap. Journ. Math., 17 (1940), 37–96.Google Scholar
[5] Tsuji, M.: On the cluster set of a meromorphic function, Proc. Imp. Acad. Tokyo, 19 (1943), pp. 60–65.Google Scholar