Several necessary and sufficient conditions for a family of Möbius maps to be a normal family in the extended complex plane \(\mathbb {C}_\infty \) are established. Each of these conditions involves collections of two or three points which may vary with the Möbius maps in the family, provided the points satisfy a uniform separation condition. In addition, we derive a sufficient condition for the normality of a family of Möbius maps in terms of the average value of the reciprocal of the chordal derivative.

中文翻译：

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莫比乌斯地图的普通家庭

建立了Möbius映射族成为扩展复杂平面\（\ mathbb {C} _ \ infty \）中的法线族的几个充要条件。这些条件中的每一个都涉及两个或三个点的集合，如果这些点满足统一的分离条件，则这些点可能随族中的Möbius地图而变化。此外，根据弦导数的倒数的平均值，我们为一族莫比乌斯图的正态性得出了充分条件。