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converges uniformly
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(Definition)
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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 $f$
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"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 43 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 9893 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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Pending Errata and Addenda
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