# pi-system

Let $\mathrm{\Omega}$ be a set, and $\mathcal{P}(\mathrm{\Omega})$ be the power set^{} of $\mathrm{\Omega}$. A *$\pi $-system* (or pi-system) on $\mathrm{\Omega}$ is a set $\mathcal{F}\subseteq \mathcal{P}(\mathrm{\Omega})$ such that

$$A,B\in \mathcal{F}\Rightarrow A\cap B\in \mathcal{F}.$$ | (1) |

A $\pi $-system is closed under finite intersection^{}.

Title | pi-system |
---|---|

Canonical name | Pisystem |

Date of creation | 2013-03-22 12:21:23 |

Last modified on | 2013-03-22 12:21:23 |

Owner | drummond (72) |

Last modified by | drummond (72) |

Numerical id | 4 |

Author | drummond (72) |

Entry type | Definition |

Classification | msc 03E20 |

Classification | msc 28A60 |

Related topic | DynkinSystem |

Related topic | SigmaAlgebra |

Related topic | DynkinsLemma |