# counting measure

Let $(X,\U0001d505)$ be a measurable space^{}. The measure^{} $\mu $ on $X$ defined by

$$\mu (A)=\{\begin{array}{cc}n\hfill & \text{if}A\text{has exactly}n\text{elements}\hfill \\ \mathrm{\infty}\hfill & \text{otherwise.}\hfill \end{array}$$ |

for all $A\in \U0001d505$ is called the counting measure on $X$. Usually this is applied when $X$ is countable, e.g. $\mathbb{N}$ or $\mathbb{Z}$.

Title | counting measure |
---|---|

Canonical name | CountingMeasure |

Date of creation | 2013-03-22 12:21:52 |

Last modified on | 2013-03-22 12:21:52 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 7 |

Author | mathwizard (128) |

Entry type | Definition |

Classification | msc 28A12 |

Related topic | Measure |