# Weierstrass approximation theorem

If $f$ is a continuous^{} real-valued function on a interval $[a,b]$
then for all $\epsilon >0$ there exists a polynomial^{} $P$
which satisfies $$
This theorem also holds for compact subsets of ${\mathbb{R}}^{n}.$
The Stone-Weierstrass theorem is a generalization^{} to even more general situations.

Title | Weierstrass approximation theorem^{} |
---|---|

Canonical name | WeierstrassApproximationTheorem |

Date of creation | 2013-03-22 14:34:52 |

Last modified on | 2013-03-22 14:34:52 |

Owner | Tobi (6409) |

Last modified by | Tobi (6409) |

Numerical id | 7 |

Author | Tobi (6409) |

Entry type | Theorem |

Classification | msc 41A10 |