# Lusin’s theorem

Let $A$ be a Lebesgue measurable subset of $\mathbb{R}$ and $f:A\to \u2102$ (or $f:A\to \mathbb{R}$). Then $f$ is Lebesgue measurable (http://planetmath.org/MeasurableFunctions) if and only if $f$ is almost continuous^{}.

Title | Lusin’s theorem |
---|---|

Canonical name | LusinsTheorem |

Date of creation | 2013-03-22 16:13:48 |

Last modified on | 2013-03-22 16:13:48 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 6 |

Author | Wkbj79 (1863) |

Entry type | Theorem |

Classification | msc 28A20 |

Related topic | MeasurableFunctions |

Related topic | AlmostContinuousFunction |