# Baroni’s theorem

Let $(x_{n})_{n\geq 0}$ be a sequence of real numbers such that $\displaystyle\lim_{n\rightarrow\infty}(x_{n+1}-x_{n})=0$. 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 $\overline{\mathbb{R}}=\mathbb{R}\bigcup\{-\infty,+\infty\}$

Title Baroni’s theorem BaronisTheorem 2013-03-22 13:32:30 2013-03-22 13:32:30 mathwizard (128) mathwizard (128) 6 mathwizard (128) Theorem msc 40A05