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Revision difference : converges uniformly |
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Version 2 |
| Let $X$ be a set, $(Y,\rho)$ a metric space and $\{f_n\}$ a sequence of functions from $X$ to $Y$, and $f:X\to Y$ another function. |
Let $X$ be a set, $(Y,\rho)$ a metric space and $\{f_n\}$ a sequence of functions from $X$ to $Y$, and $f:X\to Y$ another function. |
| If for any $\varepsilon>0$ there exists an integer $N$ such that |
If for any $\varepsilon>0$ there exists an integer $N$ such that |
| \[ \rho(f_n(x),f(x))<\varepsilon \] |
\[ \rho(f_n(x),f(x))<\varepsilon \] |
| for all $n>N$ |
for all $n>N$ |
| we say that $f_n$ converges unformly to $f$. |
we say that $f_n$ converges unformly to $f$. |
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