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Harju Jarmo Absolute branch points on Riemann surfaces 36 pp 1984
Proof of the main theorem
7 other sections not shown
a-point additive extended real-valued additive real-valued set additive set function Ai(zo,a aj,w algebroid func algebroid function determined Assume At-i cluster points conformal point Corollary 4.15 counting functions Definition 1.10 Definitions 1.5(1 denote determined by 1.1 entire functions extended real-valued set fc(zo,d function and let function on Zq G C be distinct Given a subring Hausdorff space Hence holomorphic in VZo implies infinity exponent JV(r Lemma let zo,a lim n(FJr locally finite subset meromorphic functions monotone nonincreasing nonconstant algebroid function nonconstant v-valued algebroid obtain pointwise discrete Proof Proposition 2.7 Proposition 3.23 quasi-branched points Ra(z real-valued functions real-valued or extended real-valued set function Remark ring ring of sets Satz say that n(X second fundamental inequality slit complex plane slit disk VZo Suppose that n(X taking the value Theorem 6.3 transcendental v-valued algebroid uniqueness theorem v-valued algebroid function v-valued and v-valued z0 G C zq G