# Baroni’s theorem

Let ${({x}_{n})}_{n\ge 0}$ be a sequence of real numbers such that $\underset{n\to \mathrm{\infty}}{lim}({x}_{n+1}-{x}_{n})=0$. Let $A=\{{x}_{n}|n\in \mathbb{N}\}$ and A’ the set of limit points^{} of $A$.
Then A’ is a (possibly degenerate) interval from $\overline{\mathbb{R}}$, where $\overline{\mathbb{R}}=\mathbb{R}\bigcup \{-\mathrm{\infty},+\mathrm{\infty}\}$

Title | Baroni’s theorem |
---|---|

Canonical name | BaronisTheorem |

Date of creation | 2013-03-22 13:32:30 |

Last modified on | 2013-03-22 13:32:30 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 6 |

Author | mathwizard (128) |

Entry type | Theorem |

Classification | msc 40A05 |