Difference between revisions of "Convergence in norm"
From Encyclopedia of Mathematics
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| + | 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==== | ||
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See also [[Convergence, types of|Convergence, types of]]. | See also [[Convergence, types of|Convergence, types of]]. | ||
Latest revision as of 15:33, 4 May 2012
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.
How to Cite This Entry:
Convergence in norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_norm&oldid=11744
Convergence in norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_norm&oldid=11744
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article