# converges uniformly

Let $X$ be a set, $(Y,\rho)$ a metric space and $\{f_{n}\}$ a sequence of functions from $X$ to $Y$, and $f\colon X\to Y$ another function.

If for every $\varepsilon>0$ there exists an integer $N$ such that

 $\rho(f_{n}(x),f(x))<\varepsilon$

for all $x\in X$ and all $n>N$, then we say that $f_{n}$ converges uniformly to $f$.

Title converges uniformly ConvergesUniformly 2013-03-22 14:01:23 2013-03-22 14:01:23 yark (2760) yark (2760) 10 yark (2760) Definition msc 40A30 UniformConvergence AbsoluteConvergence