## Regular growth of subharmonic functions |

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0<lim r"logM(r a)dd analogous consideration Applying the second arbitrary large value arbitrary positive bounded Borel sets branches are fixed complete the proof Const Const.n converges corres defined for bounded denote domain DR defined exists is due finite f finite plane follows FR(z FUNCTIONS By Jun-iti given gives harmonic holds hypothesis imply that 0<lim inf u(z integral function f(z Jensen's formula Jffi(f Lemma 11 let q Let u(z lim inf limsup mass distribution defined mean value theorem mK(r monotone increasing function Moreover mR(r n>l+q NAGOYA Nevanlinna formula non-integral positive real non-negative constant non-negative real number number and let oo exists open set perfectly regular growth ponding mass distribution positive real number proof of Lemma prove q be defined r-oo replaced RFK(z RFR(z Riesz mass distribution second mean value selected sufficiently large sequence small positive number SUBHARMONIC FUNCTIONS Theorem F Theorem G implies Z—l I R—Zt