# summable function

A measurable function^{} $f:\mathrm{\Omega}\to \mathbb{R}$ where $(\mathrm{\Omega},\mathcal{A},\mu )$ is a measure space^{} is said to be summable if the Lebesgue integral^{} of the absolute value^{} of $f$ exists and is finite,

$$ |

An alternative way of expressing this condition is to assert that $f\in {L}^{1}(\mathrm{\Omega})$.

Note that some authors distinguish between integrable and summable: an integrable function is one for which the above integral exists; a summable function is one for which the integral exists and is finite.

Title | summable function |
---|---|

Canonical name | SummableFunction |

Date of creation | 2013-03-22 18:12:14 |

Last modified on | 2013-03-22 18:12:14 |

Owner | ehremo (15714) |

Last modified by | ehremo (15714) |

Numerical id | 8 |

Author | ehremo (15714) |

Entry type | Definition |

Classification | msc 28A25 |

Related topic | LebesgueIntegrable |