# Fatou’s lemma

If ${f}_{1},{f}_{2},\mathrm{\dots}$ is a sequence of nonnegative measurable functions^{} in a measure space^{} $X$, then

$${\int}_{X}\underset{n\to \mathrm{\infty}}{lim\; inf}{f}_{n}\le \underset{n\to \mathrm{\infty}}{lim\; inf}{\int}_{X}{f}_{n}$$ |

Title | Fatou’s lemma |
---|---|

Canonical name | FatousLemma |

Date of creation | 2013-03-22 13:12:50 |

Last modified on | 2013-03-22 13:12:50 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 6 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 28A20 |

Related topic | FatouLebesgueTheorem |

Related topic | MonotoneConvergenceTheorem |

Related topic | DominatedConvergenceTheorem |