---
tag: 08VZ57PT26
kind: concept
name: Uniform convergence
msc: [40A30]
sources:
  - url: https://en.wikipedia.org/wiki/Uniform_convergence
    locator: lead section
same_as:
  wikidata: Q1411887
  wikipedia: Uniform convergence
---

## Summary

A sequence of functions converges uniformly when the largest distance between $f_n$ and the limit tends to zero. Uniform limits keep continuity, and they commute with integration. The node [[uniform convergence|08FPABDQ4C]] gives the precise definition.