Convergence in norm

2020 Mathematics Subject Classification: Primary: 46Bxx [MSN][ZBL]

Convergence of a sequence $(x_n)$ in a normed vector space $X$ to an element $x$, defined in the following way: $x_n \rightarrow x$ if $$\text{$\left\| x_n - x \right\| \rightarrow 0$ as $n\rightarrow\infty$.}$$ Here $\left\|\cdot\right\|$ is the norm in $X$.

Comments

See also Convergence, types of.