# almost continuous function

Let $m$ denote Lebesgue measure^{}, $A$ be a Lebesgue measurable subset of $\mathbb{R}$, and $f:A\to \u2102$ (or $f:A\to \mathbb{R}$). Then $f$ is *almost continuous ^{}* if, for every $\epsilon >0$, there exists a closed subset $F$ of $\mathbb{R}$ such that $F\subseteq A$, $$, and ${f|}_{F}$ is continuous.

Title | almost continuous function |
---|---|

Canonical name | AlmostContinuousFunction |

Date of creation | 2013-03-22 16:13:45 |

Last modified on | 2013-03-22 16:13:45 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 4 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 28A20 |

Synonym | almost continuous |

Related topic | LusinsTheorem2 |