An Overview of Uniform Convergence

A detailed tutorial of uniform convergence. Step by step tutorial including several example problems of uniform convergence for reference.

Uniform convergence is a very strong type of convergence, even stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does not depend on x. This concept is important because several properties of these functions are transferred to the limit f if the convergence is uniform.

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