# Egorov’s theorem

Let $(X,\mathcal{S},\mu )$ be a measure space^{}, and let $E$ be a subset of $X$ of finite measure. If ${f}_{n}$ is a sequence of measurable functions^{} converging to $f$ almost everywhere, then for each $\delta >0$ there exists a set ${E}_{\delta}$ such that $$ and ${f}_{n}\to f$ uniformly (http://planetmath.org/UniformConvergence) on $E-{E}_{\delta}$.

Title | Egorov’s theorem |
---|---|

Canonical name | EgorovsTheorem |

Date of creation | 2013-03-22 13:13:46 |

Last modified on | 2013-03-22 13:13:46 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 6 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 28A20 |

Synonym | Egoroff’s theorem |