0
$\begingroup$

Suppose $\{f_n\}$ be a sequence of continuous function$f_n:S\to \mathbb{R}$ where $S\subset \mathbb{R}$ and $S$ is compact. Suppose for $\{f_n(x)\}$ monotonic decreasing to zero for any $x\in S$. Is $\{f_n\}$ uniformly converge to $ 0$? I know all the definition of convergence and uniformly convergence and compact but still not sure how to start or prove it

  • 0
    Anyhow, to improve the chances of someone finding this one, I edited the title of the question.2012-12-03

1 Answers 1

2

Yes. This is known as Dini's theorem.