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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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new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

## 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