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Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions

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Ukrainian Mathematical Journal Aims and scope

We prove that the set of logarithms of moduli of entire functions of several complex variables is nowhere dense in the space of plurisubharmonic functions equipped with a topology that is a generalization of the topology of uniform convergence on compact sets. This topology is generated by a metric in which plurisubharmonic functions form a complete metric space. Thus, the logarithms of moduli of entire functions form a set of the first Baire category.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1602 – 1609, December, 2008.

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Girnyk, M.A. Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions. Ukr Math J 60, 1878–1888 (2008). https://doi.org/10.1007/s11253-009-0177-1

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  • DOI: https://doi.org/10.1007/s11253-009-0177-1

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