##  [Uniform Convergence](/uniform-convergence) 

  ##  [Uniform Convergence](https://puremath.quantumdictionary.io/uniform-convergence-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sequence f_n converges uniformly to f on a set D if sup_{x in D} |f_n(x)-f(x)| tends to zero as n→∞; the convergence is controlled by a single bound valid for all points of the domain.