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High Quality Content by WIKIPEDIA articles! In the mathematical field of analysis, uniform convergence is a type of convergence 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. The concept is important because several properties of the functions fn, such as continuity and Riemann integrability, are transferred to the limit f if the convergence is uniform.