Regular Growth of Subharmonic Functions |
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0≤lim r logM(r analogous consideration arbitrary large value arbitrary positive bounded Borel sets branches are fixed Const corres ER(z finite plane follows that lim FR(z FUNCTIONS By Jun-iti given gives GROWTH OF SUBHARMONIC harmonic Hence holds imply that 0≤lim inf r M(r integral function f(z J₁ Jensen's formula Juce K₁ K₂ largest integer Lemma 11 let 1≤q let q Let u(z lim inf logM(r lim lim lim m∞(R ma(r mass distribution defined mean value theorem Moreover MR(R NAGOYA non-negative real number number and let open set ponding mass distribution positive real number proof of Lemma q be defined r)dr converges r₁ r₂ r² t² RER(it)dt RFR(t RFR(z Riesz mass distribution second mean value selected sufficiently large sequence ß)sin SUBHARMONIC FUNCTIONS sup r logM(r sup r M(r t t r Theorem F write ηπ ίρπ π π