PlanetMath: converges uniformly

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converges uniformly

(Definition)

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

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

$\begin{displaymath}\rho(f_n(x),f(x))<\varepsilon \end{displaymath}$

for all $x\in X$ and all

, then we say that

converges uniformly to

"converges uniformly" is owned by yark. [ full author list (4) | owner history (3) ]

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Cross-references: integer, functions, sequence, metric space
There are 36 references to this entry.

This is version 7 of converges uniformly, born on 2003-10-15, modified 2006-09-17.
Object id is 4986, canonical name is ConvergesUniformly.
Accessed 7419 times total.

Classification:

AMS MSC:

40A30 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences of functions)

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