# Scheffé’s theorem

Let $X,{X}_{1},{X}_{2},\mathrm{\dots}$ be continuous random variables in a probability space^{}, whose probability density functions^{} are $f,{f}_{1},{f}_{2},\mathrm{\dots}$, respectively. If ${f}_{n}\to f$ almost everywhere (relative to Lebesgue measure^{},) then ${X}_{n}$ converges to $X$ in distribution (http://planetmath.org/ConvergenceInDistribution):
${X}_{n}\stackrel{\mathit{D}}{\to}X$.

Title | Scheffé’s theorem |
---|---|

Canonical name | ScheffesTheorem |

Date of creation | 2013-03-22 13:14:23 |

Last modified on | 2013-03-22 13:14:23 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 6 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 60E05 |