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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

Jul 5

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

Jun 11

new question: binomial coefficients: is this a known relation? by pfb

Jun 6

new question: difference of a function and a finite sum by pfb

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

Jun 11

new question: binomial coefficients: is this a known relation? by pfb

Jun 6

new question: difference of a function and a finite sum by pfb

## 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