# Krylov-Bogolubov theorem

Any continuous map^{} on a metrizable compact^{} topological space^{} has an invariant Borel probability measure (i.e. a Borel probability measure that is preserved by the given map).

Title | Krylov-Bogolubov theorem |
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Canonical name | KrylovBogolubovTheorem |

Date of creation | 2013-03-22 14:07:10 |

Last modified on | 2013-03-22 14:07:10 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 5 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 37A05 |

Classification | msc 28C15 |

Synonym | existence of invariant measures |

Synonym | Krylov-Bogoliubov |