Let be a sequence of functions, each regular in a region , let for every and in , and let tend to a limit as at a set of points having a Limit Point inside . Then tends uniformly to a limit in any region bounded by a contour interior to , the limit therefore being an analytic function of .

**References**

Titchmarsh, E. C. *The Theory of Functions, 2nd ed.* Oxford, England: Oxford University Press, p. 168, 1960.

© 1996-9

1999-05-26