容量与掩蔽定理

设G和G^~为扩充复平面C^-上的区域，且含有∞点，又设f:G→G^~为半纯函数，∞为它的ｍ级极点，令 E=C^~\G，F=C^~\G^~，显然E，F为紧集，本文给出容量capE与capF比较的两个不等式，并利用这些不等式得到了几个有趣的掩蔽定理。

Capacity and Covering Theorems

Suppose that G and G^~ are domains in C^- with ∞ included. Assume that f: G →G^~is meromorphic with a pole of order m at ∞. Let E=C^~\G and F=C^~\G^~ be compact sets. Under some conditions on f(see Theorem 1), two inequalities concerning cap E and cap F are given. By using these inequalities several covering theorems are obtained.