Convergence in norm

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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 $X$.


See also Convergence, types of.

How to Cite This Entry:
Convergence in norm. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article