# filtration

A filtration^{} is a sequence of sets ${A}_{1},{A}_{2},\mathrm{\dots},{A}_{n}$ with

$${A}_{1}\subset {A}_{2}\subset \mathrm{\cdots}\subset {A}_{n}.$$ |

If one considers the sets ${A}_{1},\mathrm{\dots},{A}_{n}$ as elements of a larger set which are partially ordered by inclusion, then a filtration is simply a finite chain with respect to this partial ordering. It should be noted that in some contexts the word “filtration” may also be employed to describe an infinite chain.

Title | filtration |
---|---|

Canonical name | Filtration |

Date of creation | 2013-03-22 12:08:38 |

Last modified on | 2013-03-22 12:08:38 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 9 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 03E20 |

Related topic | FiltrationOfSigmaAlgebras |