# Choquet’s capacitability theorem

Choquet’s capacitability theorem states that analytic sets^{} (http://planetmath.org/AnalyticSet2) are capacitable.

###### Theorem (Choquet).

Let $\mathrm{F}$ be a paving that is closed under finite unions and finite intersections^{}. If $I$ is an $\mathrm{F}$-capacity, then all $\mathrm{F}$-analytic sets are $\mathrm{(}\mathrm{F}\mathrm{,}I\mathrm{)}$-capacitable.

A useful consequence of this result for applicatons to measure theory is the universal^{} measurability of analytic sets (http://planetmath.org/MeasurabilityOfAnalyticSets).

Title | Choquet’s capacitability theorem |
---|---|

Canonical name | ChoquetsCapacitabilityTheorem |

Date of creation | 2013-03-22 18:47:49 |

Last modified on | 2013-03-22 18:47:49 |

Owner | gel (22282) |

Last modified by | gel (22282) |

Numerical id | 4 |

Author | gel (22282) |

Entry type | Theorem |

Classification | msc 28A05 |

Classification | msc 28A12 |

Synonym | capacitability theorem |