# almost periodic function (equivalent definition)

There is an equivalent^{} definition of almost periodic function due to Bochner:

A function $f:\mathbb{R}\to \mathbb{R}$ is *almost periodic* if
every sequence of translates of $f$ has a uniformly convergent subsequence.

Not only is this definition simpler to state than that of Bohr, but it also generalizes to functions on groups.

Title | almost periodic function (equivalent definition) |
---|---|

Canonical name | AlmostPeriodicFunctionequivalentDefinition |

Date of creation | 2013-03-22 15:23:03 |

Last modified on | 2013-03-22 15:23:03 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 8 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 42A75 |