TY - JOUR AU - M. A. Girnyk PY - 2008/12/25 Y2 - 2024/03/28 TI - Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 60 IS - 12 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3274 AB - 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. ER -