# atom (measure theory)

Let $(X,\mathcal{B},\mu )$ be a measure space^{}. A set $A\in \mathcal{B}$ is called an atom if $A$ has positive measure and contains no measurable subsets $B\subset A$ such that $$.

An equivalent^{} definition can be: $A$ has positive measure and for every measurable subset $B\subset A$, either $\mu (B)=0$ or $\mu (A-B)=0$.

Title | atom (measure theory) |
---|---|

Canonical name | AtommeasureTheory |

Date of creation | 2013-03-22 17:38:31 |

Last modified on | 2013-03-22 17:38:31 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 4 |

Author | asteroid (17536) |

Entry type | Definition |

Classification | msc 28A05 |

Synonym | atom |