Pointwise convergence

Description

A sequence of functions converges point-wise to another function, if all of its value converge to the value of the limit function.. (i.e. point wise)

Definition

Let $U\subseteq \mathbb{C}$ and $f_n:U\to \mathbb{C}$. $f_n$ converges point-wise if for every $x\in U$ and $ϵ>0$ there exists a $N\in \mathbb{N}$ such that $|f_n(x)-f(x)|<ϵ$ for all $n\ge N$.

Properties

Tip

Examples

Example