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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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## Recent Activity

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

new question: Lorenz system by David Bankom

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

new question: Lorenz system by David Bankom

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

## 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