##  [Lipschitz Continuity](/lipschitz-continuity) 

  ##  [Lipschitz Continuity](https://natural.quantumdictionary.io/lipschitz-continuity-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function f between metric spaces is Lipschitz continuous if there exists a constant L≥0 such that for all x,y the distance between f(x) and f(y) is at most L times the distance between x and y.

 

 

 

 

 





 

 



 ##  [Lipschitz Continuity](https://puremath.quantumdictionary.io/lipschitz-continuity-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

There exists a constant L≥0 such that for all x,y in the domain, d(f(x),f(y)) ≤ L·d(x,y). The smallest such L is called a Lipschitz constant. This provides a global linear bound on increments.