# Convergence in norm

From Encyclopedia of Mathematics

2010 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.

**How to Cite This Entry:**

Convergence in norm.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Convergence_in_norm&oldid=25986

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article