A Property of Azarin's Limit Set of Subharmonic Functions - Chouigui, A.; Grishin, A.F. (Журнал математической физики, анализа, геометрии, 2008)
Let v(z) be a subharmonic function of order ρ > 0, and Fr(v) be the limit set in the sense of Azarin. Let z be fixed and I(z) = {u(z) : u is in Fr(v)}. We prove that I(z) is either a closed interval or a semiclosed interval which does not contain its infimum.