Abstract
We prove contour-solid theorems for finely hypoharmonic functions defined in finely open sets of the complex plane.
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P. M. Tamrazov and O. A. Sarana, Contour-Solid Properties of Finely Subharmonic Functions [in Russian], Preprint No. 94.33, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1994).
P. M. Tamrazov, “Strengthened contour-solid results for subharmonic functions,” Ukr. Mat. Zh., 40, No. 2, 210–219 (1988).
M. Brelot, On Topologies and Boundaries in Potential Theory [Russian translation], Mir, Moscow (1974).
B. Fuglede, “Finely holomorphic functions. A survey,” Rev. Roum. Math. Pures Appl., 33, 283–295 (1988).
B. Fuglede, “Finely harmonic functions,” Lect. Notes Math., No. 289, Springer, Berlin (1972).
N. Bourbaki, Éléments de Mathématique. Intégration [Russian translation], Nauka, Moscow (1977).
P. M. Tamrazov, A Local Contour-Solid Problem for Subharmonic Functions [in Russian], Preprint No. 84.52, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984).
P. M. Tamrazov, Contour-Solid Problems for Holomorphic Functions and Mappings [in Russian], Preprint No. 83.65, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983).
W. K. Hayman and P. B. Kennedy, Subharmonic Functions [Russian translation], Mir, Moscow (1980).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1114–1125, August, 1997.
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Tamrazov, P.M., Sarana, A.A. Contour-solid properties of finely hypoharmonic functions. Ukr Math J 49, 1252–1264 (1997). https://doi.org/10.1007/BF02487550
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DOI: https://doi.org/10.1007/BF02487550