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# uniform convergence

*uniformly convergent* to another function $f$ if, for each $\varepsilon>0$, there exists $N$ such that, for all $x$ and all $n>N$, we have $d(f_{n}(x),f(x))<\varepsilon$.
This is denoted by $f_{n}\xrightarrow[]{u}f$, or “$f_{n}\rightarrow f$ uniformly” or, less frequently, by $f_{n}\rightrightarrows f$.

Defines:

uniformly convergent

Related:

CompactOpenTopology, ConvergesUniformly

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

40A30*no label found*

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## Attached Articles

limit function of sequence by pahio

the limit of a uniformly convergent sequence of continuous functions is continuous by neapol1s

limit laws for uniform convergence by stevecheng

uniform convergence on union interval by pahio

point preventing uniform convergence by pahio

absolute convergence implies uniform convergence by rspuzio

the limit of a uniformly convergent sequence of continuous functions is continuous by neapol1s

limit laws for uniform convergence by stevecheng

uniform convergence on union interval by pahio

point preventing uniform convergence by pahio

absolute convergence implies uniform convergence by rspuzio