Editing Uniform convergence (section)

===To analyticity===
Using [[Morera's Theorem]], one can show that if a sequence of [[Analytic function|analytic]] functions converges uniformly in a region S of the complex plane, then the limit is analytic in S. This example demonstrates that complex functions are more well-behaved than real functions, since the uniform limit of analytic functions on a real interval need not even be differentiable (see [[Weierstrass function]]).