Convergence in norm
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This category corresponds roughly to MSC {{{id}}} {{{title}}}; see {{{id}}} at MathSciNet and {{{id}}} at zbMATH.
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.
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