# converges uniformly

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

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

$$ |

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

Title | converges uniformly |
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Canonical name | ConvergesUniformly |

Date of creation | 2013-03-22 14:01:23 |

Last modified on | 2013-03-22 14:01:23 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 10 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 40A30 |

Related topic | UniformConvergence |

Related topic | AbsoluteConvergence |